Bentuk-bentuk persamaan logaritma ada apa aja, ya? Terus, gimana cara menyelesaikannya? Yuk, simak penjelasannya dalam artikel Matematika kelas 10 berikut!
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Kalian pasti udah tau dong, kalo gempa itu adalah gelombang atau getaran yang merambat dan aktivitasnya bisa direkam pakai seismograf? Nah, tapi kamu tau nggak sih, gimana caranya seseorang menentukan intensitas gempa?
Jadi, intensitas gempa itu bisa diukur dengan skala richter. Skala ini menggunakan prinsip dari logaritma dengan basis 10.
Sebenarnya, masih banyak sih, contoh penerapan prinsip logaritma yang lainnya, misalnya taraf intensitas bunyi, mengukur pH atau tingkat asam suatu zat, dan lain sebagainya.
Nah, pas banget nih, sama materi yang bakal kita bahas kali ini, yaitu persamaan logaritma.
Untuk materi logaritmanya sendiri, mungkin rata-rata dari kalian belum pernah belajar ya, waktu di SMP dulu. Tapi, walaupun materi ini baru kalian temuin di SMA, materinya seru dan nggak susah kok!
Sebelum kita ke pembahasan persamaan logaritma, make sure kamu harus udah paham konsep awal logaritma. Tapi, kalo kamu masih belum jelas, coba kamu check artikel tersebut, ya.
Oke, kalo gitu langsung aja kita mulai pembahasan persamaan logaritma!
Pengertian Persamaan Logaritma
Persamaan logaritma adalah persamaan yang memuat bentuk logaritma dengan basis atau numerus, atau keduanya memuat variabel.
Jadi maksudnya, ada dua bentuk logaritma (di ruas kiri dan kanan) dimana basis atau numerus atau keduanya memuat variabel, kemudian kedua ruas ini dihubungan dengan tanda sama dengan. Nilai x yang memenuhi persamaan ini disebut dengan penyelesaian dari persamaan tersebut.
Sebelumnya, masih inget kan sama bentuk umum logaritma yang ini:
alog x = n
a = basis atau bilangan pokok, dengan syarat a > 0 dan a≠1
x = numerus, dengan syarat x > 0
n = nilai logaritma
Terus, kalau persamaan logaritma bentuknya gimana ya?
Bentuknya sama seperti bentuk umum logaritma, tapi pada persamaan logaritma, bentuk logaritmanya ada dua di ruas kiri dan kanan lalu dihubungkan menggunakan tanda sama dengan. Contohnya seperti ini, nih:
3log (2x+9) = 3log (10x – 16)
Nanti kita akan bahas lebih lanjut ya, gimana caranya untuk mendapatkan nilai x yang memenuhi persamaan tersebut. Tapi sebelum itu, kita bahas bentuk-bentuk persamaan logaritma dulu, ya!
Baca Juga: Cara Menyelesaikan Persamaan & Pertidaksamaan Eksponen
Bentuk-Bentuk Persamaan Logaritma
Nggak jauh beda dari materi eksponen, persamaan logaritma juga punya beberapa bentuk yang bikin kamu lebih gampang untuk mengidentifikasi nilai peubahnya. Nah, ini dia bentuk-bentuk persamaan logaritma:
Wah, keliatannya ribet ya. Tapi padahal nggak sesusah itu kok. Sederhananya, logaritma memiliki enam bentuk seperti yang bisa kamu lihat pada gambar di atas.
Bentuk Pertama
Sekarang kita coba bahas mulai dari bentuk yang pertama, yaitu alog f(x) = alog n. Coba perhatikan gambar berikut!
Nah, supaya kamu lebih paham, kita langsung masuk ke contoh soal ya, sekalian kita belajar gimana cara menyelesaikan persamaannya.
Contoh soal:
Tentukan nilai x yang memenuhi persamaan logaritma berikut ini:
- 3log (3x+6) = 3log 9
- 2log (x+9) = 5
Jawab:
a. 3log (3x+6) = 3log 9
Karena basis dari logaritmanya nilainya sama, maka nilai numerusnya juga akan sama. Sehingga bisa kita tulis seperti berikut:
Kemudian, kita bisa uji numerus, jadi kita substitusi x = 1 ke 3x + 6.
3x + 6 = 3(1) + 6 = 9
Nah, ketemu nih, hasilnya adalah 9, di mana 9 > 0, maka syarat numerus f(x) > 0 terpenuhi. Jadi, penyelesaian 3log (3x+6) = 3log 9 adalah x = 1.
b. 2log (x+9) = 5
Nah, untuk menyelesaikan persamaan ini, kita ubah ruas kanan ke bentuk logaritma terlebih dahulu, dengan memilih nilai basis yang sama dengan ruas kiri, dan memanfaatkan sifat alog bc = c alog b. Maka menjadi seperti berikut:
2log (x+9) = 5 x 2log 2
2log (x+9) = 2log 25 (5 kita pindah sebagai pangkat dan ini nggak mengubah nilai, hanya mengubah bentuknya aja)
Lanjut, kita uji numerus, (x+9) = 23 + 9 = 32, karena 32 > 0, maka syarat terpenuhi. Jadi, nilai x yang memenuhi persamaan 2log (x+9) = 5 adalah 23.
Sekarang kita lanjut ke bentuk persamaan logaritma yang kedua, yuk!
Baca Juga: Cara Menyelesaikan Persamaan & Pertidaksamaan Linear Mutlak
Bentuk Kedua
Bentuk persamaan logaritma yang kedua, hampir sama dengan bentuk yang pertama tadi, tapi numerusnya berbeda.
Kita langsung kerjakan contoh soal, ya!
Contoh soal:
Tentukan nilai x yang memenuhi persamaan log (x2 – 2x – 15) = log (x + 3)!
Jawab:
Nah, sampai disini kita bisa uji syarat numerus.
Walau g(x) > 0 tapi f(x) = 0, jadi x = -3 tidak memenuhi persamaan logaritma ini. Lanjut untuk x = 6.
-
Untuk x = 6
f(x) = x2-2x-15 = (6)2-2(6)-15 = 9
g(x) = x2+3= (6)2+3 = 39
Memenuhi karena f(x) dan g(x) > 0.
Jadi, nilai x yang memenuhi persamaan log (x2-2x-15) = log (x+3) adalah x = 6.
Sekarang, lanjut ke bentuk ketiga!
Bentuk Ketiga
Untuk bentuk persamaan logaritma yang ketiga, bentuknya adalah seperti infografik di bawah ini. Coba perhatikan!
Di persamaan ketiga ini numerusnya sama, tapi basisnya berbeda.
Contoh soal:
Tentukan nilai x yang memenuhi persamaan 2log (5x-9) = 5log (5x-9)!
Jawab:
Karena numerus sama yaitu 5x – 9 dan kedua basis nilainya lebih dari 0, berarti sudah dipastikan numerus = 1.
Kita bisa melakukan uji numerus, 5x – 9 = 5(2) – 9 = 1 di mana 1 > 0 dan syarat terpenuhi. Penyelesaian dari 2log(5x-9) = 5log(5x-9) persamaan adalah x = 2. Gimana seru kann? yuk kita bahas bentuk selanjutnya!
Baca Juga: Perbedaan Persamaan Linear dan Pertidaksamaan Linear
Bentuk Keempat
Oke guys, kita udah sampai di bentuk persamaan logaritma yang keempat. Perhatikan infografik di bawah.
Persamaan ini hampir mirip kayak bentuk persamaan nomor 2. Bedanya, basis sama numerus punya variabel, tapi basis di kiri dan kanan tetap sama ya, kaya gini nih!
Contoh soal:
Tentukan nilai x yang memenuhi persamaan x-1log (x2-16) = x-1log (5x-2)!
Jawab:
kemudian kita faktorkan (x – 7) ( x + 2) diperoleh x = 7 dan x = -2
Lalu kita uji syarat basis dan numerusnya, agar lebih mudah kita pakai tabel aja ya.
Karena x = 7 menghasilkan numerus x2 – 7 dan 5x -2 yang lebih dari 0, kemudian basis x-1 yang lebih dari 0 dan tidak sama dengan 1, maka hanya x = 7 yang memenuhi syarat logaritmanya. Jadi, penyelesaian dari persamaan ini adalah x = 7.
Bentuk Kelima
Nah, untuk bentuk kelima, kamu bisa perhatikan infografik berikut. Jangan lupa perhatikan syaratnya juga, ya!
Untuk bentuk kelima ini, tipenya seperti bentuk yang sebelumnya (memiliki variabel di numerus dan basis), tapi basis di kiri dan kanan berbeda.
Contoh soal:
Tentukan penyelesaian persamaan x+3log (x2-5) = 2x-1log (x2-5)!
Jawab:
Lanjut kita uji syarat basis dan numerusnya, ya!
- Uji Numerus
Memenuhi syarat karena numerus > 0
- Saat x2 – 5 = 1, maka x = ±√6
Tapi, yang memenuhi hanya √6 saja karena hanya nilai √6 yang memenuhi syarat basis dan numerus.
Oke, kita udah dapet nih, penyelesaian persamaan x+3log (x2-5) = 2x-1log (x2-5) yaitu x = 4.
Baca Juga: Memahami Fungsi Trigonometri Sederhana
Bentuk Keenam
Bentuk keenam atau bentuk terakhir ini agak berbeda dari persamaan sebelumnya ya, karena bentuk persamaan logaritma ini membentuk persamaan kuadrat. Perhatikan infografik berikut ini ya:
Supaya kamu bisa nyelesain persamaan yang dikasih, tugas kamu harus memisalkan logaritma jadi bentuk. Nah, dari permisalan itu, kamu bakal dapet bentuk persamaan kuadratnya.
Contoh soal:
Tentukan penyelesaian persamaan 3log2 x – 3log x3 – 4 = 0!
Jawab:
Walau dari bentuk umum tandanya plus, tapi kita bisa menjumpai soal yang tandanya minus seperti halnya persamaan kuadrat,
3log2 x – 3log x3 – 4 = 0 bisa juga ditulis dengan 3log2 x+ (-3log x3) + (-4)
Jadi, gak ada masalah ya untuk tanda plus dan minus, yang penting kamu fokus di basis dan numerusnya.
Oke, supaya kita dapet nilai x-nya, langsung aja kita substitusi nilai y ke permisalan.
Wahhh, akhirnya selesai juga nih bahasan kita tentang bentuk-bentuk persamaan logaritma dan cara menyelesaikannya. Sekarang kamu udah lebih ngerti, kan? Intinya, kamu harus mengingat syarat-syarat dari masing-masing bentuk. Jangan sampai tertukar!
Oh ya, setelah baca ini jangan langsung bobo yaa hehehe, karena kamu harus banget latihan soal di ruangbelajar. Pemahaman kamu tentang persamaan logaritma ini bakal lebih keren lagi deh, karena fitur di ruangbelajar lengkap banget, mulai dari latihan soal yang selalu update dan juga pembahasan yang asik plus mudah dimengerti dari Master Teacher. So, tunggu apalagi? Yuk, ke ruangbelajar!
Referensi:
Sinaga, B. (2014). Matematika SMA/MA Kelas X Semester 1. Jakarta: Pusat Perbukuan, Departemen Pendidikan Nasional.
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<h1 class="content-title">
Bentuk-Bentuk Persamaan Logaritma dan Cara Menyelesaikannya | Matematika Kelas 10 </h1>
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<p class="content-author"><a href="https://www.ruangguru.com/blog/author/kak-efira-mt-saintek" class="">Kak Efira MT Saintek</a> </p>
<p class="content-info"><span>July 23, 2025 • </span> <span>7 minutes read</span></p>
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<p><img decoding="async" class="aligncenter size-medium" src="https://cdn-web-2.ruangguru.com/landing-pages/assets/7b5b8cb7-4324-4c34-873d-aa511d280e2b.png" alt="bentuk persamaan logaritma dan cara menyelesaikannya" width="820" /></p>
<blockquote>
<p style="text-align: center; font-size: 16px;"><em>Bentuk-bentuk persamaan logaritma ada apa aja, ya? Terus, gimana cara menyelesaikannya? Yuk, simak penjelasannya dalam <strong><a href="https://www.ruangguru.com/blog/c/matematika/matematika-sma-kelas-10">artikel Matematika kelas 10</a></strong> berikut!</em></p>
<p style="text-align: center; font-size: 16px;"><em>—</em></p>
</blockquote>
<p> </p>
<p style="text-align: justify;">Kalian pasti udah tau dong, kalo gempa itu adalah gelombang atau getaran yang merambat dan aktivitasnya bisa direkam pakai seismograf? Nah, tapi kamu tau nggak sih, gimana caranya seseorang menentukan intensitas gempa?</p>
<p style="text-align: justify;">Jadi, intensitas gempa itu bisa diukur dengan <span style="font-weight: bold;">skala richter.</span> Skala ini menggunakan prinsip dari <span style="font-weight: bold;">logaritma dengan basis 10</span>.</p>
<p style="text-align: justify;">Sebenarnya, masih banyak sih, contoh penerapan prinsip logaritma yang lainnya, misalnya taraf intensitas bunyi, mengukur pH atau tingkat asam suatu zat, dan lain sebagainya.</p>
<p style="text-align: justify;">Nah, pas banget nih, sama materi yang bakal kita bahas kali ini, yaitu <span style="font-weight: bold;">persamaan logaritma</span>.</p>
<p style="text-align: justify;">Untuk materi logaritmanya sendiri, mungkin rata-rata dari kalian belum pernah belajar ya, waktu di SMP dulu. Tapi, walaupun materi ini baru kalian temuin di SMA, materinya seru dan nggak susah kok!</p>
<p style="text-align: justify;">Sebelum kita ke pembahasan persamaan logaritma, <em>make sure</em> kamu harus udah paham <a href="/blog/mengenal-logaritma-dan-sifat-sifatnya" rel="noopener"><span style="font-weight: bold;">konsep awal logaritma</span></a>. Tapi, kalo kamu masih belum jelas, coba kamu <span style="font-style: italic;">check</span> artikel tersebut, ya.</p>
<p style="text-align: justify;">Oke, kalo gitu langsung aja kita mulai pembahasan persamaan logaritma!</p>
<p> </p>
<h2><span style="font-size: 18pt;">Pengertian Persamaan Logaritma</span></h2>
<p style="text-align: justify;">Persamaan logaritma adalah <span style="font-weight: bold;">persamaan yang memuat bentuk logaritma dengan basis atau numerus, atau keduanya memuat variabel</span>.</p>
<p style="text-align: justify;">Jadi maksudnya, ada <span style="font-weight: bold;">dua bentuk logaritma</span> <span style="font-weight: bold;">(di ruas kiri dan kanan)</span> dimana basis atau numerus atau keduanya memuat variabel, kemudian kedua ruas ini dihubungan dengan tanda sama dengan. Nilai x yang memenuhi persamaan ini disebut dengan penyelesaian dari persamaan tersebut.</p>
<p>Sebelumnya, masih inget kan sama <span style="font-weight: bold;">bentuk umum logaritma</span> yang ini:</p>
<p style="text-align: center; font-size: 18px;"><strong><sup>a</sup>log x = n</strong></p>
<p style="text-align: justify;">a = basis atau bilangan pokok, dengan syarat a > 0 dan a≠1<br />
x = numerus, dengan syarat x > 0<br />
n = nilai logaritma</p>
<p> </p>
<p style="text-align: justify;">Terus, kalau <span style="font-weight: bold;">persamaan logaritma</span> bentuknya gimana ya?</p>
<p style="text-align: justify;">Bentuknya sama seperti bentuk umum logaritma, tapi pada persamaan logaritma, bentuk logaritmanya <span style="font-weight: bold;">ada dua</span> di ruas kiri dan kanan lalu dihubungkan menggunakan <span style="font-weight: bold;">tanda sama dengan</span>. Contohnya seperti ini, nih:</p>
<p style="text-align: center; font-size: 16px; font-weight: bold;"><sup>3</sup>log (2x+9) = <sup>3</sup>log (10x – 16)</p>
<p> </p>
<p style="text-align: justify;">Nanti kita akan bahas lebih lanjut ya, gimana caranya untuk mendapatkan nilai x yang memenuhi persamaan tersebut. Tapi sebelum itu, kita bahas bentuk-bentuk persamaan logaritma dulu, ya!</p>
<p><strong>Baca Juga: <a href="https://www.ruangguru.com/blog/matematika-kelas-10-cara-menyelesaikan-persamaan-dan-pertidaksamaan-eksponen">Cara Menyelesaikan Persamaan & Pertidaksamaan Eksponen</a></strong></p>
<p> </p>
<h2><span style="font-size: 18pt;">Bentuk-Bentuk Persamaan Logaritma</span></h2>
<p style="text-align: justify;">Nggak jauh beda dari materi <strong><a href="/blog/matematika-kelas-10-cara-menyelesaikan-persamaan-dan-pertidaksamaan-eksponen" rel="noopener">eksponen</a></strong>, persamaan logaritma juga punya beberapa bentuk yang bikin kamu lebih gampang untuk mengidentifikasi nilai peubahnya. Nah, ini dia bentuk-bentuk persamaan logaritma:</p>
<p><img decoding="async" style="width: 600px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/6%20bentuk%20persamaan%20logaritma.jpg" alt="6 bentuk persamaan logaritma" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Wah, keliatannya ribet ya. Tapi padahal nggak sesusah itu kok. Sederhananya, logaritma memiliki enam bentuk seperti yang bisa kamu lihat pada gambar di atas.</p>
<p> </p>
<h3><span style="font-size: 14pt;">Bentuk Pertama</span></h3>
<p style="text-align: justify;">Sekarang kita coba bahas mulai dari bentuk yang pertama, yaitu <sup>a</sup>log f(x) = <sup>a</sup>log n. Coba perhatikan gambar berikut!</p>
<p><img decoding="async" style="width: 600px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/bentuk%20persamaan%20logaritma%201.jpg" alt="bentuk persamaan logaritma 1" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Nah, supaya kamu lebih paham, kita langsung masuk ke contoh soal ya, sekalian kita belajar gimana cara menyelesaikan persamaannya.</p>
<p style="text-align: justify; font-weight: bold;">Contoh soal:</p>
<p style="text-align: justify;">Tentukan nilai x yang memenuhi persamaan logaritma berikut ini:</p>
<ol style="list-style-type: lower-alpha;">
<li style="text-align: justify;"><sup style="background-color: transparent; text-align: left;">3</sup><span style="background-color: transparent; font-size: 1rem; text-align: left;">log (3x+6) = </span><sup style="background-color: transparent; text-align: left;">3</sup><span style="background-color: transparent; font-size: 1rem; text-align: left;">log 9</span></li>
<li style="text-align: justify;"><sup>2</sup>log (x+9) = 5</li>
</ol>
<p> </p>
<p style="text-align: justify; font-weight: bold;">Jawab:</p>
<p style="text-align: justify;">a. <sup>3</sup>log (3x+6) = <sup>3</sup>log 9</p>
<p style="text-align: justify;">Karena basis dari logaritmanya nilainya sama, maka nilai numerusnya juga akan sama. Sehingga bisa kita tulis seperti berikut:</p>
<p style="text-align: justify;"><img decoding="async" class="aligncenter" style="width: 278px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/1-Sep-29-2021-06-54-59-60-AM.png" alt="1-Sep-29-2021-06-54-59-60-AM" width="278" /></p>
<p> </p>
<p style="text-align: justify;">Kemudian, kita bisa <strong>uji numerus</strong><span style="font-weight: normal;">, jadi kita substitusi x = 1 ke 3x + 6</span>.</p>
<p style="text-align: justify;">3x + 6 = 3(1) + 6 = 9</p>
<p style="text-align: justify;"><span style="font-weight: normal;">Nah, ketemu nih,</span> <span style="font-weight: normal;">hasilnya adalah 9, di mana </span><strong>9 > 0</strong>, <span style="font-weight: normal;">maka</span><strong> syarat numerus f(x) > 0 terpenuhi. </strong>Jadi, penyelesaian <sup>3</sup>log (3x+6) = <sup>3</sup>log 9 adalah <span style="font-weight: bold;">x = 1</span>.</p>
<p> </p>
<p style="text-align: justify;">b. <span style="background-color: transparent;"><sup>2</sup>log (x+9) = 5</span></p>
<p style="text-align: justify;">Nah, untuk menyelesaikan persamaan ini, kita <span style="font-weight: bold;">ubah ruas kanan ke bentuk logaritma </span><span style="font-weight: normal;">terlebih dahulu</span>, dengan memilih nilai basis yang sama dengan ruas kiri, dan memanfaatkan sifat <sup>a</sup>log b<sup>c</sup> = c <sup>a</sup>log b. Maka menjadi seperti berikut:</p>
<p style="text-align: justify;"><sup>2</sup>log (x+9) = 5 x <sup>2</sup>log 2</p>
<p style="text-align: justify;"><sup>2</sup>log (x+9) = <sup>2</sup>log 2<sup>5</sup> <span style="font-weight: normal;">(5 kita pindah sebagai pangkat dan ini nggak mengubah nilai, hanya mengubah bentuknya aja)</span></p>
<p style="text-align: justify;"><strong><img decoding="async" class="aligncenter" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Nov-20-2020-07-42-40-84-AM.png" /></strong></p>
<p> </p>
<p style="text-align: justify;"><span style="font-weight: normal;">Lanjut, kita </span><strong>uji numerus</strong>, (x+9) = 23 + 9 = 32, <strong>karena 32 > 0, maka syarat terpenuhi</strong><span style="font-weight: normal;">. Jadi,</span> <span style="background-color: transparent; font-size: 1rem;">nilai x yang memenuhi persamaan </span><span style="background-color: transparent; position: relative; font-size: 12px; line-height: 0; vertical-align: baseline; top: -0.5em;">2</span><span style="background-color: transparent; font-size: 1rem;">log (x+9) = 5 adalah <span style="font-weight: bold;">23</span>.</span></p>
<p style="text-align: justify;">Sekarang kita lanjut ke bentuk persamaan logaritma yang kedua, yuk!</p>
<p><strong>Baca Juga: <a href="https://www.ruangguru.com/blog/menyelesaikan-persamaan-dan-pertidaksamaan-linear-mutlak">Cara Menyelesaikan Persamaan & Pertidaksamaan Linear Mutlak</a></strong></p>
<p> </p>
<h3><span style="font-size: 14pt;">Bentuk Kedua</span></h3>
<p style="text-align: justify;">Bentuk persamaan logaritma yang kedua, hampir sama dengan bentuk yang pertama tadi, <strong>tapi numerusnya berbeda.</strong></p>
<p><img decoding="async" style="width: 600px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/bentuk%20persamaan%20logaritma%202.jpg" alt="bentuk persamaan logaritma 2" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Kita langsung kerjakan contoh soal, ya!</p>
<p style="text-align: justify; font-weight: bold;">Contoh soal:</p>
<p style="text-align: justify; font-weight: normal;">Tentukan nilai x yang memenuhi persamaan log (x<sup>2</sup> – 2x – 15) = log (x + 3)!</p>
<p style="text-align: justify; font-weight: bold;">Jawab:</p>
<p style="text-align: justify;"><img decoding="async" class="aligncenter" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Nov-20-2020-07-48-33-13-AM.png" /></p>
<p> </p>
<p style="text-align: justify;">Nah, sampai disini kita bisa<strong> uji syarat numerus</strong>.</p>
<ul style="text-align: justify;">
<li><span style="font-weight: bold;">Untuk x = – 3</span>
<p style="text-align: justify;">f(x) = x<sup>2 </sup>– 2x -15 = (-3)<sup>2 </sup>– 2(- 3) -15 = 0<br />
<span style="background-color: transparent;">g(x) = x<sup>2 </sup>+ 3 = (-3)<sup>2</sup>+3 = 12</span></p>
</li>
</ul>
<p> </p>
<p style="text-align: justify;"><strong>Walau g(x) > 0 tapi f(x) = 0, jadi x = -3 tidak memenuhi persamaan logaritma ini. Lanjut untuk x = 6.</strong></p>
<ul style="text-align: justify;">
<li><strong>Untuk x = 6</strong><br />
f(x) = x<sup style="background-color: transparent;">2</sup><span style="background-color: transparent;">-2x-15 = (6)</span><sup style="background-color: transparent;">2</sup><span style="background-color: transparent;">-2(6)-15 = 9</span><br />
g(x) = x<sup style="background-color: transparent;">2</sup><span style="background-color: transparent;">+3= (6)</span><sup style="background-color: transparent;">2</sup><span style="background-color: transparent;">+3 = 39</span></li>
</ul>
<p> </p>
<p style="text-align: justify;"><strong>Memenuhi karena f(x) dan g(x) > 0.</strong></p>
<p style="text-align: justify;">Jadi, nilai x yang memenuhi persamaan log (x<sup>2</sup>-2x-15) = log (x+3) adalah x = 6.</p>
<p style="text-align: justify;">Sekarang, lanjut ke bentuk ketiga!</p>
<p> </p>
<h3><span style="font-size: 14pt;">Bentuk Ketiga</span></h3>
<p style="text-align: justify;">Untuk bentuk persamaan logaritma yang ketiga, bentuknya adalah seperti infografik di bawah ini. Coba perhatikan!</p>
<p><img decoding="async" style="width: 600px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/bentuk%20persamaan%20logaritma%203.jpg" alt="bentuk persamaan logaritma 3" width="600" /></p>
<p> </p>
<p>Di persamaan ketiga ini numerusnya sama, tapi <strong>basisnya berbeda.</strong></p>
<p style="text-align: justify; font-weight: bold;">Contoh soal:</p>
<p style="text-align: justify;">Tentukan nilai x yang memenuhi persamaan <sup>2</sup>log (5x-9) = <sup>5</sup>log (5x-9)!</p>
<p style="text-align: justify; font-weight: bold;">Jawab:</p>
<p style="text-align: justify;">Karena<strong> numerus sama</strong> yaitu 5x – 9 dan<strong> kedua basis nilainya lebih dari 0, berarti sudah dipastikan numerus = 1</strong>.</p>
<div style="text-align: justify;"><img decoding="async" class="aligncenter" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Nov-20-2020-08-01-07-49-AM.png" /></div>
<div></div>
<p style="text-align: justify;">Kita bisa melakukan uji numerus, 5x – 9 = 5(2) – 9 = 1 di mana 1 > 0 dan syarat terpenuhi. Penyelesaian dari <sup>2</sup>log(5x-9) = <sup>5</sup>log(5x-9) persamaan adalah x = 2. Gimana seru kann? yuk kita bahas bentuk selanjutnya!</p>
<p><strong>Baca Juga: <a href="https://www.ruangguru.com/blog/perbedaan-persamaan-linear-dan-pertidaksamaan-linear">Perbedaan Persamaan Linear dan Pertidaksamaan Linear</a></strong></p>
<p> </p>
<h3><span style="font-size: 14pt;">Bentuk Keempat</span></h3>
<p style="text-align: justify;">Oke <em>guys</em>, kita udah sampai di bentuk persamaan logaritma yang keempat. Perhatikan infografik di bawah.</p>
<p><img decoding="async" style="width: 600px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/bentuk%20persamaan%20logaritma%204.jpg" alt="bentuk persamaan logaritma 4" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Persamaan ini hampir mirip kayak bentuk persamaan nomor 2. Bedanya, <strong>basis sama numerus punya variabel,</strong> tapi basis di kiri dan kanan tetap sama ya, kaya gini nih!</p>
<p style="text-align: justify; font-weight: bold;">Contoh soal:</p>
<p style="text-align: justify;">Tentukan nilai x yang memenuhi persamaan <sup>x-1</sup>log (x<sup>2</sup>-16) = <sup>x-1</sup>log (5x-2)!</p>
<p style="text-align: justify; font-weight: bold;">Jawab:</p>
<p style="text-align: justify;"><img decoding="async" class="aligncenter" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Nov-20-2020-08-09-49-45-AM.png" /></p>
<p> </p>
<p style="text-align: justify;">kemudian kita faktorkan (x – 7) ( x + 2) diperoleh x = 7 dan x = -2</p>
<p style="text-align: justify;"><strong>Lalu kita uji syarat basis dan numerusnya</strong>, agar lebih mudah kita pakai tabel aja ya.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/numerus%20dan%20basis%20persamaan%20logaritma.jpg" alt="numerus dan basis persamaan logaritma" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Karena x = 7 menghasilkan numerus x<sup>2</sup> – 7 dan 5x -2 yang lebih dari 0, kemudian basis x-1 yang lebih dari 0 dan tidak sama dengan 1, maka hanya x = 7 yang memenuhi syarat logaritmanya. Jadi, penyelesaian dari persamaan ini adalah <span style="font-weight: bold;">x = 7</span>.</p>
<p> </p>
<h3><span style="font-size: 14pt;">Bentuk Kelima</span></h3>
<p><span style="color: #000000;">Nah, untuk bentuk kelima, kamu bisa perhatikan infografik berikut. Jangan lupa perhatikan syaratnya juga, ya!</span></p>
<p><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/persamaan%20logaritma.jpg" alt="persamaan logaritma" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Untuk bentuk kelima ini, tipenya seperti bentuk yang sebelumnya (memiliki variabel di numerus dan basis), tapi <span style="font-weight: bold;">basis di kiri dan kanan berbeda</span>.</p>
<p style="text-align: justify; font-weight: bold;">Contoh soal:</p>
<p style="text-align: justify;">Tentukan penyelesaian persamaan <sup>x+3</sup>log (x<sup>2</sup>-5) = <sup>2x-1</sup>log (x<sup>2</sup>-5)!</p>
<p style="text-align: justify; font-weight: bold;">Jawab:</p>
<p style="text-align: justify;"><img decoding="async" class="aligncenter" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Nov-20-2020-08-19-07-17-AM.png" /></p>
<p> </p>
<p style="text-align: justify;">Lanjut kita <strong>uji syarat basis dan numerus</strong><span style="font-weight: bold;">nya</span><span style="font-weight: normal;">,</span> ya!</p>
<ul style="text-align: justify;">
<li>Uji Basis<br />
<img decoding="async" style="background-color: transparent;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Nov-20-2020-08-19-43-93-AM.png" /></li>
</ul>
<p> </p>
<ul style="text-align: justify;">
<li>Uji Numerus<br />
<img decoding="async" style="background-color: transparent;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Nov-20-2020-08-20-55-92-AM.png" /><br />
Memenuhi syarat karena numerus > 0</li>
</ul>
<p> </p>
<ul style="text-align: justify;">
<li style="text-align: justify;">Saat x<sup>2 </sup>– 5 = 1, maka x = ±√6<br />
Tapi, yang memenuhi hanya √6 saja karena hanya nilai √6 yang memenuhi syarat basis dan numerus.</li>
</ul>
<p> </p>
<p style="text-align: justify;">Oke, kita udah dapet nih, penyelesaian persamaan <sup>x+3</sup>log (x<sup>2</sup>-5) = <sup>2x-1</sup>log (x<sup>2</sup>-5) yaitu x = 4.</p>
<p><strong>Baca Juga: <a href="https://www.ruangguru.com/blog/memahami-fungsi-trigonometri-sederhana">Memahami Fungsi Trigonometri Sederhana</a></strong></p>
<p> </p>
<h3><span style="font-size: 14pt;">Bentuk Keenam</span></h3>
<p style="text-align: justify;">Bentuk keenam atau bentuk terakhir ini agak berbeda dari persamaan sebelumnya ya, karena bentuk persamaan logaritma ini membentuk persamaan kuadrat. Perhatikan infografik berikut ini ya:</p>
<p style="text-align: justify;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/bentuk-bentuk%20persamaan%20logaritma.jpg" alt="bentuk-bentuk persamaan logaritma" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Supaya kamu bisa nyelesain persamaan yang dikasih, tugas kamu harus memisalkan logaritma jadi bentuk. Nah, dari permisalan itu, kamu bakal dapet bentuk persamaan kuadratnya.</p>
<p style="text-align: justify; font-weight: bold;">Contoh soal:</p>
<p style="text-align: justify;">Tentukan penyelesaian persamaan <sup>3</sup>log<sup>2 </sup>x – <sup>3</sup>log x<sup>3 </sup>– 4 = 0!</p>
<p style="text-align: justify; font-weight: bold;">Jawab:</p>
<p style="text-align: justify;">Walau dari bentuk umum tandanya plus, tapi kita bisa menjumpai soal yang tandanya minus seperti halnya persamaan kuadrat,</p>
<p style="text-align: justify;"><sup>3</sup>log<sup>2 </sup>x – <sup>3</sup>log x<sup>3 </sup>– 4 = 0 bisa juga ditulis dengan <sup>3</sup>log<sup>2 </sup>x+ (-<sup>3</sup>log x<sup>3</sup>) + (-4)</p>
<p style="text-align: justify;">Jadi, <strong>gak ada masalah ya untuk tanda plus dan minus, yang penting kamu fokus di basis dan numerusnya.</strong></p>
<p style="text-align: justify;"><img decoding="async" class="aligncenter" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Nov-20-2020-08-29-13-04-AM.png" /></p>
<p> </p>
<p style="text-align: justify;">Oke, <strong>supaya kita dapet nilai x-nya, langsung aja kita substitusi nilai y ke permisalan.</strong></p>
<ul style="text-align: justify;">
<li><strong>Untuk y = 4</strong><br />
<img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Nov-20-2020-08-30-31-08-AM.png" /></li>
<li><strong>Untuk y = -1</strong><br />
<img decoding="async" style="width: 489px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Nov-20-2020-08-32-17-69-AM.png" width="489" /></li>
</ul>
<p> </p>
<p style="text-align: justify;">Wahhh, akhirnya selesai juga nih bahasan kita tentang bentuk-bentuk persamaan logaritma <span style="background-color: transparent; font-size: 1rem;">dan cara menyelesaikannya</span><span style="background-color: transparent; font-size: 1rem;">. Sekarang kamu udah lebih ngerti, kan? </span><span style="background-color: transparent; font-size: 1rem;">Intinya, kamu harus mengingat syarat-syarat dari masing-masing bentuk. Jangan sampai tertukar!</span></p>
<p style="text-align: justify;">Oh ya, setelah baca ini jangan langsung bobo yaa hehehe, karena kamu harus banget latihan soal di ruangbelajar. Pemahaman kamu tentang persamaan logaritma ini bakal lebih keren lagi deh, karena fitur di ruangbelajar lengkap banget, mulai dari latihan soal yang selalu <span style="font-style: italic;">update</span> dan juga pembahasan yang asik plus mudah dimengerti dari <em>Master Teacher</em>. <em>So</em>, tunggu apalagi? Yuk, ke <a href="https://www.ruangguru.com/ruangbelajar" target="_blank" rel="noopener"><span style="font-weight: bold;">ruangbelajar</span></a>!</p>
<p style="text-align: justify;"><a href="https://bayar.ruangguru.com/"><img decoding="async" class="aligncenter size-medium" src="https://cdn-web-2.ruangguru.com/landing-pages/assets/ceb472c4-1feb-4a1d-afdf-4f92234a63d0.jpg" alt="CTA Ruangguru" /></a></p>
<p style="text-align: justify;"><strong>Referensi:</strong></p>
<p style="text-align: left;">Sinaga, B. (2014). <em>Matematika SMA/MA Kelas X Semester 1</em>. Jakarta: Pusat Perbukuan, Departemen Pendidikan Nasional.</p>
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<img class="icon-call-us" src="https://cdn-web-2.ruangguru.com/file-uploader/lp/4b58468a-b2f9-40e4-867f-d3242a065dcf.png" loading="lazy" alt="Logo Whatsapp Footer" />0815 7441 0000</a>
</address>
</nav>
<nav class="footer-menu social d-none d-lg-block">
<p class="title">Ikuti Kami</p>
<a target="_blank" href="https://www.instagram.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/instagram.png" loading="lazy" alt="Logo Instagram Footer" width="32px" height="32px" />
</picture>
</a>
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<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60&convert=webp" type="image/webp">
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</picture>
</a>
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<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/twitter.png" loading=" lazy" alt="Logo Twitter Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.youtube.com/ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/youtube.png" loading=" lazy" alt="Logo Youtube Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.linkedin.com/company/ruangguru-com">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/linkedin.png" loading=" lazy" alt="Logo LinkedIn Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.tiktok.com/@ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/tiktok.png" loading=" lazy" alt="Logo TikTok Footer" width="32px" height="32px" />
</picture>
</a>
</nav>
</div>
<div class="col-lg-9">
<div class="row">
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Produk Ruangguru</p>
<ul type="none">
<li><a href="https://roboguru.ruangguru.com" target="_blank">Roboguru</a></li>
<li><a href="https://www.ruangguru.com/roboguruplus">Roboguru Plus</a></li>
<li><a href="https://www.ruangguru.com/dafa-lulu">Dafa dan Lulu</a></li>
<li><a href="https://www.ruangguru.com/for-kids/kursus">Kursus for Kids</a></li>
<li><a href="https://www.ruangguru.com/for-kids">Ruangguru for Kids</a></li>
<li><a href="https://www.ruangguru.com/bisnis">Ruangguru for Business</a></li>
<li><a href="https://www.ruangguru.com/ruanguji">Ruanguji</a></li>
<li><a href="https://www.ruangguru.com/blog">Ruangbaca</a></li>
<li><a href="https://www.ruangguru.com/ruangkelas">Ruangkelas</a></li>
<li><a href="https://www.ruangguru.com/ruangbelajar">Ruangbelajar</a></li>
<li><a href="https://pengajar.ruangguru.com/">Ruangpengajar</a></li>
<li><a href="https://www.ruangguru.com/privat">Ruangguru Privat</a></li>
<li><a href="https://www.ruangpeduli.org/" target="_blank">Ruangpeduli</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Bantuan & Panduan</p>
<ul type="none">
<li><a href="https://www.ruangguru.com/company-credentials">Company Credentials</a></li>
<li><a href="https://www.ruangguru.com/beasiswa">Beasiswa Ruangguru</a></li>
<li><a href="https://www.ruangguru.com/cicilan">Cicilan Ruangguru</a></li>
<li><a href="https://www.ruangguru.com/promo">Promo Ruangguru</a></li>
<li><a href="https://ticketing.ruangguru.com/help?request_type_id=459" target="_blank">Vulnerability Report</a></li>
<li><a href="https://www.ruangguru.com/bantuan#layanan">Layanan Pengaduan</a></li>
<li><a href="https://www.ruangguru.com/terms-conditions">Syarat & Ketentuan</a></li>
<li><a href="https://www.ruangguru.com/privacy-policy">Kebijakan Privasi</a></li>
<li><a href="https://www.ruangguru.com/about-us">Tentang Kami</a></li>
<li><a href="https://www.ruangguru.com/contact-us">Kontak Kami</a></li>
<li><a href="https://www.ruangguru.com/press">Press Kit</a></li>
<li><a href="https://www.ruangguru.com/bantuan">Bantuan</a></li>
<li><a href="https://career.ruangguru.com/">Karier</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Produk Lainnya</p>
<ul type="none">
<li><a href="https://www.brainacademy.id/" target="_blank">Brain Academy</a></li>
<li><a href="https://www.english-academy.id/" target="_blank">English Academy</a></li>
<li><a href="https://skillacademy.com/" target="_blank">Skill Academy</a></li>
<li><a href="https://www.ruangkerja.id/" target="_blank">Ruangkerja</a></li>
<li><a href="https://www.schoters.com/id/" target="_blank">Schoters</a></li>
<li><a href="https://www.kalananti.id/" target="_blank">Kalananti</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title"> Coba GRATIS Aplikasi Ruangguru</p>
<div class="download-list">
<ul>
<li>
<a target="_blank" rel="nofollow" href="https://apps.apple.com/id/app/ruangguru-solusi-belajar/id1099742206?l=id">
<img src="https://cdn-web-2.ruangguru.com/static/appstore.png" loading="lazy" alt="Button App Store Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://play.google.com/store/apps/details?id=com.ruangguru.livestudents&hl=in">
<img src="https://cdn-web-2.ruangguru.com/static/googleplay.png" loading="lazy" alt="Button Google Play Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://appgallery.huawei.com/#/app/C102352375">
<img src="https://cdn-web-2.ruangguru.com/static/huawei.png" loading="lazy" alt="Button AppGallery Footer " />
</a>
</li>
</ul>
</div>
</nav>
</div>
</div>
</div>
</div>
<div class="d-lg-none text-center">
<nav class="footer-menu social">
<p class="title">Ikuti Kami</p>
<a target="_blank" href="https://www.instagram.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/instagram.png" loading="lazy" alt="Logo Instagram Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.facebook.com/ruanggurucom/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/facebook.png" loading="lazy" alt="Logo Facebook Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://twitter.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/twitter.png" loading=" lazy" alt="Logo Twitter Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.youtube.com/ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/youtube.png" loading=" lazy" alt="Logo Youtube Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.linkedin.com/company/ruangguru-com">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/linkedin.png" loading=" lazy" alt="Logo LinkedIn Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.tiktok.com/@ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/tiktok.png" loading=" lazy" alt="Logo TikTok Footer" width="32px" height="32px" />
</picture>
</a>
</nav>
</div>
<p class="footer-copyright">
© 2026 All Rights Reserved PT. Ruang Raya Indonesia
</p>
</div>
<style>
.bantuan-container {
position: relative;
}
.bantuan-element {
position: fixed;
z-index: 999;
display: flex;
align-items: flex-end;
justify-content: flex-end;
cursor: pointer;
transition: all 0.6s ease;
}
.bantuan-top {
bottom: 11rem;
right: 2rem;
}
.bantuan-bottom {
bottom: 2rem;
right: 2rem;
}
.bantuan-top-2 {
bottom: 15rem;
right: 2rem;
}
.bantuan-top-3 {
bottom: 19rem;
right: 2rem;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 2rem;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 2rem;
}
@media (min-width: 768px) {
.bantuan-element img {
width: auto;
transition: all 0.4s ease;
}
.bantuan-top img {
width: 140px;
}
.bantuan-bottom img {
width: 140px;
}
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 140px;
}
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 140px;
}
.bantuan-element.clicked {
bottom: 9rem;
right: 2.5rem;
}
.bantuan-element.clicked img {
width: auto;
height: 64px;
}
}
@media (max-width: 767px) {
.bantuan-top {
bottom: 8rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom {
bottom: 2rem;
right: 1.25rem;
align-items: center;
}
.bantuan-top-2 {
bottom: 12rem;
right: 1rem;
align-items: center;
}
.bantuan-top-3 {
bottom: 16rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 1.25rem;
align-items: center;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 1.25rem;
align-items: center;
}
.bantuan-element img {
width: auto;
}
.bantuan-top img,
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 96px;
}
.bantuan-bottom img,
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 96px;
}
}
.bantuan-element:hover {
transform: scale(1.05);
}
.bantuan-element img {
max-width: 100%;
height: auto;
}
</style>
<div id="bantuan-divs-container" style="position: relative" data-product="ruangguru" data-table="rg_floating_icon"></div>
<script>
class FloatingDivsComponent {
constructor(product = 'ruangguru', table = 'rg_floating_icon') {
this.container = document.getElementById('bantuan-divs-container');
this.floatingElements = [];
this.product = product;
this.table = table;
// Configuration
this.config = {
baseApiUrl: 'https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/rg_banner/views/',
apiKey: 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
maxElements: 2,
zIndexBase: 100,
};
// Build dynamic API URL based on table parameter
this.config.apiUrl = this.buildApiUrl();
this.init();
}
buildApiUrl() {
const baseUrl = this.config.baseApiUrl;
const tableName = this.table || 'rg_floating_icon';
const queryParams =
'offset=0&limit=99999&sort=rankPosition&where=(type,eq,floating)~and(showIn,anyof,blog)~and(hide,is,false)~and(product,eq,' +
this.product +
')&nested%5Bcta%5D%5Bfields%5D=Id,name,ctaId,imageUrl,ctaLink,targetUrl';
return `${baseUrl}${tableName}?${queryParams}`;
}
async init() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to initialize floating divs component:', error);
}
}
async fetchFloatingElements() {
try {
const options = {
method: 'GET',
headers: {
'xc-token': this.config.apiKey || 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
},
};
const urlNoco = this.config.apiUrl;
const response = await fetch(urlNoco, options);
if (!response.ok) {
throw new Error(`HTTP error! status: ${response.status}`);
}
const data = await response.json();
this.floatingElements = this.processApiResponse(data);
} catch (error) {
console.error('Error fetching floating elements:', error);
throw error;
}
}
processApiResponse(data) {
if (!data || !data.list || !Array.isArray(data.list)) {
return [];
}
console.log(data.list);
// Ensure we only get maximum 2 elements
const limitedElements = data.list.slice(0, this.config.maxElements);
return limitedElements;
}
renderFloatingElements() {
if (!this.container || this.floatingElements.length === 0) {
return;
}
// Additional safeguard: ensure we never render more than maxElements
const elementsToRender = this.floatingElements.slice(0, this.config.maxElements);
// Clean up existing elements and their event listeners
this.cleanupExistingElements();
// Clear existing content
this.container.innerHTML = '';
elementsToRender.forEach((element, index) => {
const floatingDiv = this.createFloatingDiv(element, index);
this.container.appendChild(floatingDiv);
});
}
cleanupExistingElements() {
// Clear existing elements (no need for event listener cleanup with CSS approach)
const existingElements = this.container.querySelectorAll('[data-floating-element]');
existingElements.forEach(element => {
element.remove();
});
}
createFloatingDiv(element, index) {
const div = document.createElement('div');
const cta = element.cta[0]; // Use the first CTA
// Add data attribute for cleanup tracking
div.setAttribute('data-floating-element', 'true');
// Apply CSS classes based on rankPosition
const positionClass = this.getPositionClass(element.rankPosition, index);
div.className = `bantuan-element ${positionClass}`;
div.style.zIndex = this.config.zIndexBase + index;
// Create the link and image
const link = document.createElement('a');
link.href = 'https://cta.ruangguru.com/' + cta.ctaId || '#';
link.target = '_blank';
// Add tracking attributes
link.setAttribute('data-tracking-event-type', 'landing_page__core__item_click');
link.setAttribute(
'data-tracking-context',
JSON.stringify({
product_name: this.product,
cta_action: 'redirection',
cta_action_detail: link.href,
item_type: 'floating',
item_name: element.name || 'Floating element',
item_category: 'payment',
item_position: index,
item_serial: null,
section_type: 'floating_item',
section_position: 'body',
section_name: 'floating_item',
})
);
const img = document.createElement('img');
img.src = element.imageUrl + '?h=200&convert=webp';
img.alt = element.name || 'Floating element';
img.loading = 'lazy';
// Add click tracking
link.addEventListener('click', () => {
this.trackClick(element, cta);
});
link.appendChild(img);
div.appendChild(link);
return div;
}
getPositionClass(rankPosition, index) {
// Define positioning classes based on rankPosition
if (rankPosition === 1) {
return 'bantuan-top'; // Top position
} else if (rankPosition === 2) {
return 'bantuan-bottom'; // Bottom position
} else {
// For additional elements, distribute them evenly
return `bantuan-${index % 2 === 0 ? 'top' : 'bottom'}-${Math.floor(index / 2) + 1}`;
}
}
trackClick(element, cta) {
// Implement click tracking logic here
console.log('Floating element clicked:', {
elementId: element.Id,
elementName: cta.name,
ctaId: cta.ctaId,
targetUrl: cta.targetUrl,
});
}
// Public method to manually refresh
async refresh() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to refresh floating elements:', error);
throw error;
}
}
// Public method to get current floating elements
getFloatingElements() {
return [...this.floatingElements];
}
}
// Initialize the component when DOM is ready
document.addEventListener('DOMContentLoaded', () => {
// Get product and table parameters from data attributes
const container = document.getElementById('bantuan-divs-container');
const product = container.getAttribute('data-product') || 'ruangguru';
const table = container.getAttribute('data-table') || 'rg_floating_icon';
new FloatingDivsComponent(product, table);
});
// Export for use in other modules if needed
if (typeof module !== 'undefined' && module.exports) {
module.exports = FloatingDivsComponent;
}
</script> <div id="wp-install-nudge" style="
position: fixed;
bottom: 0rem;
right: 0;
z-index: 999;
cursor: pointer;
"></div>
<script>
(function (w, d, s, o, f, js, fjs) {
w['Sales-Nudge-Widget'] = o; w[o] = w[o] || function () { (w[o].q = w[o].q || []).push(arguments) };
js = d.createElement(s), fjs = d.getElementsByTagName(s)[0];
js.id = o; js.src = f; js.async = 1; fjs.parentNode.insertBefore(js, fjs);
}(window, document, 'script', 'wpInstallNudge', 'https://cdn-web-2.ruangguru.com/sales-nudge/6198a95130/dist/widget.js'));
wpInstallNudge('init', { targetElementId: 'wp-install-nudge', clientTarget: 'ruangguru_blog' });
</script>
<script>
// note: disabled due to auto reload page
// var lastScrollTop = 0;
// $(window).scroll(function(event){
// var st = $(this).scrollTop();
// if (st > lastScrollTop){
// $('#wp-install-nudge').slideDown( "slow", function() {});
// } else {
// $('#wp-install-nudge').slideUp( "slow", function() {});
// }
// lastScrollTop = st;
// });
// $(document).ready(function () {
// $("#wp-install-nudge").hide();
// });
$('#wp-install-nudge').click(function(){
Analytics.track("promotion__install_nudge__click",
{
user_email: "ruangguru@blog.com",
cta_link: widgetData.dataConfig.target_link
}).catch((err) => {
console.log("tracker error", err);
});
});
</script>
</footer>
<div id="__next"></div>
<script type="speculationrules">
{"prefetch":[{"source":"document","where":{"and":[{"href_matches":"\/blog\/*"},{"not":{"href_matches":["\/blog\/wp-*.php","\/blog\/wp-admin\/*","\/blog\/wp-content\/uploads\/*","\/blog\/wp-content\/*","\/blog\/wp-content\/plugins\/*","\/blog\/wp-content\/themes\/ruangguru\/*","\/blog\/*\\?(.+)"]}},{"not":{"selector_matches":"a[rel~=\"nofollow\"]"}},{"not":{"selector_matches":".no-prefetch, .no-prefetch a"}}]},"eagerness":"conservative"}]}
</script>
<script>
async function getCtaDetails(ctaIds) {
const endpoint =
" https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/CTA/views/CTA?offset=0&limit=10&where=(ctaId,in," + ctaIds.toString() + ")";
try {
const response = await fetch(endpoint, {
headers: {
"xc-token": "-hG2nBDJzSj0agSgNtcJx97M4F02y54nUMoY6plJ",
},
});
const data = await response.json();
const ctaList = data?.list || [];
const ctaMap = new Map();
for (const ctaData of ctaList) {
ctaMap.set(ctaData.ctaId, ctaData);
}
return ctaMap;
} catch (error) {
console.error("Error fetching CTA details:", error);
return new Map();
}
}
async function replaceCTA() {
const regex = /{{cta\((‘(.*?)’|“(.*?)”)\)}}/g;
const bodyHTML = document.body.innerHTML;
const matches = Array.from(bodyHTML.matchAll(regex));
const ctaIds = matches.map((match) => {
let ctaId = match[2] ?? match[3];
return ctaId;
});
const ctaMap = await getCtaDetails(ctaIds);
const replacedHTML = bodyHTML.replace(regex, (match, _inner, ctaId1, ctaId2) => {
const ctaId = ctaId1 ?? ctaId2;
const ctaData = ctaMap.get(ctaId);
if (ctaData) {
return `<a href="https://cta.ruangguru.com/${ctaData.ctaId}" target="_${ctaData.targetType}" style="position:relative;display:inline-block;">
<img src="${ctaData.imageUrl}" loading="lazy" alt="${ctaData.altText}" />
</a>`;
} else {
return match;
}
});
document.body.innerHTML = replacedHTML;
}
</script>
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</body>
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