Pada artikel Matematika kelas 10 kali ini, kamu akan mempelajari tentang logaritma, sifat-sifat logaritma, dan contohnya. Yuk, simak artikelnya berikut ini!
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Pada pembahasan sebelumnya, kamu telah mempelajari tentang dasar-dasar bilangan berpangkat (eksponen). Tentunya setelah itu, kamu jadi paham dan mahir dong ya dalam menentukan hasil dari suatu bilangan yang dipangkatkan.
Nah, materi yang akan kita bahas kali ini adalah kebalikan dari materi eksponen yang sebelumnya telah kamu pelajari. Apakah itu? Yap! Logaritma. Jadi, kalau di eksponen kamu disuruh mencari hasil pangkat, maka di logaritma kamu akan menentukan besar pangkat.
TIIDAAAAAXXX…!!! (Sumber: giphy.com)
Eits, tenang dulu. Materi ini tidak sesulit seperti yang kamu pikirkan, kok. Artikel ini akan membantu kamu untuk memahami logaritma dengan cara yang lebih mudah. So, daripada semakin penasaran, langsung saja yuk, kita simak pembahasannya bersama-sama!
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Pengertian Logaritma
Sebelumnya, mari kita ketahui dulu apa itu logaritma. Logaritma adalah suatu invers atau kebalikan dari pemangkatan (eksponen) yang digunakan untuk menentukan besar pangkat dari suatu bilangan pokok.
Jadi intinya, dengan mempelajari logaritma, kita bisa mencari besar pangkat dari suatu bilangan yang diketahui hasil pangkatnya.
“Loh, bukannya mencari besar pangkat itu mudah, ya? Misalnya, 2 pangkat berapa yang hasilnya 8, jawabannya pasti 3. Kenapa harus pusing-pusing belajar logaritma?”
Yeee… kalau itu sih memang mudah karena bilangan yang memiliki pangkat dan bilangan hasil pemangkatannya itu sama-sama merupakan bilangan bulat. Tapi, bagaimana jika salah satunya ada yang desimal? Contohnya, 5 pangkat berapa yang hasilnya 2.236? Hayooo…
Nah loh! Bingung, kan?
Oleh sebab itu, logaritma membantu kita untuk menemukan jawabannya.
Sekarang kalian paham kan, kenapa harus mempelajari materi logaritma? Selain itu, perlu kamu ketahui juga nih, materi logaritma ini tidak hanya digunakan di bidang studi matematika saja loh, tapi juga di bidang studi lain, seperti menentukan orde reaksi dalam ilmu laju reaksi kimia, menentukan koefisien serap bunyi dalam ilmu akustik, dan masih banyak lagi. Nyesel nggak sih kalau kamu nggak benar-benar paham dengan materi ini?
Hmmm… benar juga (Sumber: giphy.com)
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Sudah tahu belum, di Aplikasi belajar Ruangguru, ada fitur Drill Soal yang berisi kumpulan contoh soal latihan beserta pembahasannya, loh. Pas banget kan buat mempersiapkan diri kamu dalam menghadapi ujian nanti. Yuk, klik banner di bawah ini untuk coba fitur Drill Soal!
Bentuk Umum Logaritma
Oke, kita lanjut ya. Setelah kamu tahu apa itu logaritma, kamu juga harus tahu kalau logaritma itu memiliki bentuk umum. Seperti apa bentuk umum logaritma? Mari kita lihat pada gambar berikut ini!
Sekarang, kita perhatikan contoh di bawah ini dulu yuk agar kamu semakin paham.
Contoh:
1. Jika 32 = 9, maka dalam bentuk logaritma akan menjadi 3log 9 = 2
2. Jika 23 = 8, maka dalam bentuk logaritma akan menjadi 2log 8 = 3
3. Jika 53 = 125, maka dalam bentuk logaritma akan menjadi 5log 125 = 3
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Gimana? Sudah mulai paham, kan? Nah, biasanya nih, kamu masih akan sering bingung untuk menentukan mana angka yang menjadi basis dan mana angka yang menjadi numerus. Iya nggak?
Tenang, guys! Kuncinya, kamu ingat saja kalau bilangan pokok itu basis, letaknya di atas sebelum tanda ‘log’ dan bilangan hasil pangkat itu numerus, letaknya di bawah setelah kata ‘log’. Mudah, kan?
Contoh Penerapan Logaritma dalam Kehidupan Sehari-Hari
Meskipun logaritma terkesan susah dan ribet, tapi ternyata logaritma ini bisa diterapkan dalam kehidupan sehari-hari, lho! Antara lain digunakan untuk:
- Menentukan orde reaksi dalam ilmu laju reaksi kimia.
- Menentukan koefisien serap bunyi dalam ilmu akustik.
- Menghitung bunga bank.
- Menghitung laju pertumbuhan penduduk.
- Membantu kerja alat pengukur kekuatan gempa atau seismograf.
- Mengukur tingkat keterangan bintang.
- Menghitung kondisi keuangan.
Oke, sekarang kita lanjut belajar sifat-sifat logaritma dan contohnya, yuk!
Logaritma juga memiliki sifat-sifat yang wajib kamu pahami, nih. Kenapa wajib? Oh ya jelas, karena sifat-sifat inilah yang akan menjadi bekal kamu untuk mengerjakan soal-soal logaritma. Tanpa memahami sifat-sifat logaritma, kamu tidak akan bisa mengerjakan soal-soal logaritma, lho!
Lalu, apa saja sih sifat-sifat logaritma dan contohnya? Yuk, kita simak pada gambar di bawah ini!
“Duh, kenapa banyak banget sih sifat-sifat logaritma itu? Males ih ngafalinnya. Ribet!”
Eits… jangan salah, semua sifat di atas pasti bisa kamu kuasai dengan mudah, kok. Caranya, kamu bisa memperbanyak latihan soal tentang logaritma. Tentunya, di aplikasi Ruangguru, dong. Hehehe…
Baca Juga: Bentuk-Bentuk Persamaan Logaritma dan Cara Menyelesaikannya
Oke, supaya kamu jadi paham sifat-sifat logaritma di atas dipakai untuk model soal seperti apa, ayo kita coba kerjakan soal di bawah ini. Kita kerjakan bersama-sama, ya!
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Gimana, kamu sudah cukup paham tentang materi logaritma? Sebelum lanjut ke contoh-contoh soal logaritma, misalnya kamu mau mempelajari materi logaritma bareng ahlinya, boleh banget gabung di Ruangguru Privat Matematika.
Di Ruangguru Privat, kamu akan dimentori oleh guru-guru berkualitas yang sudah terstandarisasi. Kamu juga bebas mau pilih belajar secara tatap muka (offline) atau lewat daring (online). Fleksibel banget, kan. Yuk langsung daftar sekarang!
Contoh Soal Logaritma dan Pembahasannya
Sekarang, kita coba kerjakan contoh soal logaritma, ya! Perhatikan soal berikut:
Pembahasan:
Soal 1
Pada soal nomor 1, hal pertama yang harus kita lakukan adalah cek basisnya. Kedua persamaan logaritma di atas, ternyata memiliki nilai basis yang sama, yaitu 2.
Nah, karena basisnya sama, kita bisa menggunakan sifat logaritma yang kedua nih, untuk mengetahui hasilnya. Sehingga, 2log 4 + 2log 8 = 2log (4 × 8) = 2log 32 = 5.
Ingat! tujuan logaritma adalah mencari pangkat. Jadi, 2 pangkat berapa yang hasilnya 32? Jawabannya adalah 5. Mudah, ya? Kita lanjut ke soal nomor 2, yuk!
Soal 2
Pada soal nomor 2 ini, kita tidak bisa langsung mengerjakannya karena kamu pasti akan bingung untuk mencari nilai pangkat dari 8 yang hasilnya 32. Lalu bagaimana?
Kalau kita perhatikan soalnya dengan jeli, 8 itu merupakan hasil pemangkatan dari 23 dan 32 merupakan hasil pemangkatan dari 25. Sehingga, bentuk logaritmanya bisa kita ubah menjadi seperti berikut:
Soal 3
Gimana? sudah mulai greget? Nah, soal nomor 3 ini akan membuat kamu semakin gregetan lagi, nih! Perlu kamu ketahui, model soal nomor 3 akan sering kamu temui pada soal-soal ujian maupun soal-soal seleksi Perguruan Tinggi, lho.
Kelihatannya memang cukup rumit ya, tapi jika kamu telah paham konsepnya, soal ini akan jadi sangat mudah untuk dikerjakan. Jika kamu menemui model soal seperti ini, kamu bisa menyelesaikannya menggunakan sifat logaritma nomor 4.
Sehingga, pengerjaannya akan menjadi seperti berikut:
Note: Untuk memilih basis, kita lihat saja angka yang paling sering muncul pada soal. Angka 2 muncul sebanyak 2 kali, 8 sebanyak 1 kali, dan 7 sebanyak 1 kali. Angka yang paling banyak muncul adalah 2, sehingga kita pilih 2 sebagai basis. Paham, ya?
Selanjutnya, kita uraikan numerusnya. Usahakan kita ubah kebentuk yang sudah ada pada soal. Maksudnya gimana? Begini, di soal diketahui 2log 8 dan 2log 7. Karena numerusnya 8 dan 7, kita uraikan 14 menjadi 7 × 2 dan 16 menjadi 8 × 2 agar kita bisa ketahui hasil akhirnya.
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Setelah kamu memahami ketiga contoh soal di atas, bagaimana menurutmu? Ternyata logaritma bukanlah materi yang sulit untuk dipahami, ya.
Kamu juga perlu ingat nih, karena tujuan logaritma adalah mencari pangkat, maka modal pertama yang harus kamu miliki adalah hafal perkalian. Setelah itu, kamu juga harus paham dengan sifat-sifat logaritma. Jangan lupa untuk perbanyak latihan soal agar kamu semakin mantap lagi, nih.
Oh ya, di bawah ini ada latihan soal yang bisa kamu kerjakan. Bagi yang tahu, jangan ragu untuk tulis jawabanmu di kolom komentar ya!
Wah, menarik ya pembahasan kali ini. Bagi kamu yang masih kurang paham, kamu bisa lho, belajar lebih lanjut di ruangbelajar. Belajar jadi mudah dan praktis di mana saja dan kapan saja. Yuk, buruan download aplikasinya sekarang!
Referensi:
Sinaga, B. Sinambela, P. N. J. M. Sitanggang, A. K. dkk. (2014). Matematika. Jakarta: Kemendikbud.
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<h1 class="content-title">
Mengenal Logaritma, Sifat-Sifat, dan Contohnya | Matematika Kelas 10 </h1>
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<p class="content-author"><a href="https://www.ruangguru.com/blog/author/hani-ammariah" class="">Hani Ammariah</a> </p>
<p class="content-info"><span>July 10, 2025 • </span> <span>7 minutes read</span></p>
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<p style="text-align: justify;"><em><img decoding="async" style="height: auto; max-width: 100%; width: 820px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Logaritma%20dan%20Sifat-Sifatnya.jpg" alt="Logaritma dan Sifat-Sifatnya" /></em></p>
<blockquote>
<p style="text-align: center;"><em>Pada artikel <strong><a href="https://www.ruangguru.com/blog/c/matematika-sma-kelas-10" rel="noopener">Matematika kelas 10</a></strong> kali ini, kamu akan mempelajari tentang logaritma, sifat-sifat logaritma, dan contohnya. Yuk, simak artikelnya berikut ini!</em></p>
<p style="text-align: center;"><span style="color: #000000;">—</span></p>
</blockquote>
<p> </p>
<p style="text-align: justify;">Pada pembahasan sebelumnya, kamu telah mempelajari tentang <strong><a href="/blog/dasar-dasar-mengetahui-apa-itu-eksponen" rel="noopener">dasar-dasar bilangan berpangkat (eksponen)</a></strong>. Tentunya setelah itu, kamu jadi paham dan mahir dong ya dalam menentukan hasil dari suatu bilangan yang dipangkatkan.</p>
<p style="text-align: justify;">Nah, materi yang akan kita bahas kali ini adalah <strong>kebalikan dari materi eksponen</strong> yang sebelumnya telah kamu pelajari. Apakah itu? Yap! <strong>Logaritma</strong>. Jadi, kalau di eksponen kamu disuruh mencari hasil pangkat, maka di logaritma kamu akan menentukan besar pangkat.</p>
<p style="text-align: center;"><span style="color: #000000;"><img decoding="async" style="width: 480px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/giphy%20(5)-2.gif" alt="logaritma dan sifat-sifatnya" width="480" /></span></p>
<p style="text-align: center;"><em>TIIDAAAAAXXX…!!! (Sumber: giphy.com)</em></p>
<p> </p>
<p style="text-align: justify;">Eits, tenang dulu. Materi ini tidak sesulit seperti yang kamu pikirkan, kok. Artikel ini akan membantu kamu untuk memahami logaritma dengan cara yang lebih mudah. So, daripada semakin penasaran, langsung saja yuk, kita simak pembahasannya bersama-sama!</p>
<p style="text-align: justify;"><strong>Baca Juga: <a href="/blog/matematika-kelas-10-membuat-fungsi-kuadrat-dari-grafik" rel="noopener">Cara Menyusun Persamaan dari Grafik Fungsi Kuadrat</a></strong></p>
<p> </p>
<h2><span style="font-size: 18pt;">Pengertian Logaritma</span></h2>
<p style="text-align: justify;">Sebelumnya, mari kita ketahui dulu apa itu logaritma. <strong>Logaritma adalah suatu invers atau kebalikan dari pemangkatan (eksponen)</strong> yang <strong>digunakan untuk menentukan besar pangkat dari suatu bilangan pokok</strong>.</p>
<p style="text-align: justify;">Jadi intinya, dengan mempelajari logaritma, kita bisa mencari besar pangkat dari suatu bilangan yang diketahui hasil pangkatnya.</p>
<p style="text-align: justify;"><em>“Loh, bukannya mencari besar pangkat itu mudah, ya? Misalnya, 2 pangkat berapa yang hasilnya 8, jawabannya pasti 3. Kenapa harus pusing-pusing belajar logaritma?”</em></p>
<p style="text-align: justify;">Yeee… kalau itu sih memang mudah karena bilangan yang memiliki pangkat dan bilangan hasil pemangkatannya itu sama-sama merupakan bilangan bulat. Tapi, bagaimana jika salah satunya ada yang desimal? Contohnya, 5 pangkat berapa yang hasilnya 2.236? Hayooo…</p>
<p style="text-align: justify;">Nah loh! Bingung, kan?</p>
<p style="text-align: justify;">Oleh sebab itu, logaritma membantu kita untuk menemukan jawabannya.</p>
<p style="text-align: justify;">Sekarang kalian paham kan, kenapa harus mempelajari materi logaritma? Selain itu, perlu kamu ketahui juga nih, materi logaritma ini tidak hanya digunakan di bidang studi matematika saja loh, tapi juga di bidang studi lain, seperti menentukan orde reaksi dalam ilmu <strong><a href="/blog/pengertian-dan-faktor-yang-memengaruhi-laju-reaksi" rel="noopener">laju reaksi kimia</a></strong>, menentukan koefisien serap bunyi dalam ilmu akustik, dan masih banyak lagi. Nyesel nggak sih kalau kamu nggak benar-benar paham dengan materi ini?</p>
<p style="text-align: center;"><span style="color: #000000;"><img decoding="async" style="width: 271px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/giphy%20(7).gif" alt="logaritma dan sifat-sifatnya" width="271" /></span></p>
<p style="text-align: center;"><em>Hmmm… benar juga (Sumber: giphy.com)</em></p>
<p style="text-align: center;">—</p>
<p style="text-align: center;"><em>Sudah tahu belum, di Aplikasi belajar Ruangguru, ada fitur Drill Soal yang berisi kumpulan contoh soal latihan beserta pembahasannya, loh. Pas banget kan buat mempersiapkan diri kamu dalam menghadapi ujian nanti. Yuk, klik banner di bawah ini untuk coba fitur Drill Soal! </em></p>
<p><a href="https://link.ruangguru.com/blPk/drillsoal20"><img decoding="async" class="aligncenter size-medium" src="https://roboguru-forum-cdn.ruangguru.com/image/c2c1718a-346a-471a-b761-b0a50adcfa50.png" alt="Fitur Drill Soal Ruangguru" /></a></p>
<p> </p>
<h2><span style="font-size: 18pt;">Bentuk Umum Logaritma</span></h2>
<p style="text-align: justify;">Oke, kita lanjut ya. Setelah kamu tahu apa itu logaritma, kamu juga harus tahu kalau logaritma itu memiliki <span style="font-weight: bold;">bentuk umum</span>. Seperti apa bentuk umum logaritma? Mari kita lihat pada gambar berikut ini!</p>
<p><img fetchpriority="high" decoding="async" style="height: auto; max-width: 100%; width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Bentuk%20Umum%20Logaritma.jpg" alt="Bentuk Umum Logaritma" width="600" height="400" /></p>
<p> </p>
<p>Sekarang, kita perhatikan contoh di bawah ini dulu <em>yuk</em> agar kamu semakin paham.</p>
<p style="text-align: justify;"><strong>Contoh:</strong></p>
<p style="text-align: justify;">1. Jika 3<sup>2</sup> = 9, maka dalam bentuk logaritma akan menjadi <sup>3</sup>log 9 = 2</p>
<p style="text-align: justify;">2. Jika 2<sup>3</sup> = 8, maka dalam bentuk logaritma akan menjadi <sup>2</sup>log 8 = 3</p>
<p style="text-align: justify;">3. Jika 5<sup>3</sup> = 125, maka dalam bentuk logaritma akan menjadi <sup>5</sup>log 125 = 3</p>
<p><strong>Baca Juga: <a href="/blog/memahami-fungsi-trigonometri-sederhana" rel="noopener">Yuk, Pahami Fungsi Trigonometri Sederhana!</a></strong></p>
<p style="text-align: justify;">Gimana? Sudah mulai paham, <em>kan</em>? <em>Nah</em>, biasanya <em>nih</em>, kamu masih akan sering bingung untuk menentukan mana angka yang menjadi basis dan mana angka yang menjadi numerus. Iya nggak?</p>
<p style="text-align: justify;">Tenang, <em>guys</em>! Kuncinya, kamu ingat saja kalau <strong>bilangan pokok</strong> itu <strong>basis</strong>, <strong>letaknya di atas sebelum tanda ‘log’</strong> dan <strong>bilangan</strong> <strong>hasil pangkat</strong> itu <strong>numerus</strong>, <strong>letaknya di bawah setelah kata ‘log’</strong>. Mudah, <em>kan</em>?</p>
<p> </p>
<h2><span style="font-size: 18pt;">Contoh Penerapan Logaritma dalam Kehidupan Sehari-Hari</span></h2>
<p style="text-align: justify;">Meskipun logaritma terkesan susah dan ribet, tapi ternyata logaritma ini bisa diterapkan dalam kehidupan sehari-hari, lho! Antara lain digunakan untuk:</p>
<ul>
<li style="text-align: justify;">Menentukan orde reaksi dalam ilmu laju reaksi kimia.</li>
<li style="text-align: justify;">Menentukan koefisien serap bunyi dalam ilmu akustik.</li>
<li>Menghitung bunga bank.</li>
<li style="text-align: justify;">Menghitung laju pertumbuhan penduduk.</li>
<li>Membantu kerja alat pengukur kekuatan gempa atau seismograf.</li>
<li>Mengukur tingkat keterangan bintang.</li>
<li style="text-align: justify;">Menghitung kondisi keuangan.</li>
</ul>
<p> </p>
<p style="text-align: justify;">Oke, sekarang kita lanjut belajar sifat-sifat logaritma dan contohnya, yuk!</p>
<p> </p>
<h2><span style="font-size: 18pt;">Sifat-Sifat Logaritma</span></h2>
<p style="text-align: justify;"><span style="background-color: transparent;">Logaritma juga memiliki sifat-sifat yang <strong>wajib</strong> kamu pahami, <em>nih</em>. Kenapa wajib? Oh ya jelas, karena sifat-sifat inilah yang akan menjadi bekal kamu untuk <span style="font-weight: bold;">mengerjakan soal-soal logaritma</span>. Tanpa memahami sifat-sifat logaritma, kamu tidak akan bisa mengerjakan soal-soal logaritma, <em>lho</em>! </span></p>
<p style="text-align: justify;"><span style="background-color: transparent;">Lalu, apa saja <em>sih</em> sifat-sifat logaritma dan contohnya? <em>Yuk</em>, kita simak pada gambar di bawah ini!</span></p>
<p><img decoding="async" style="height: auto; max-width: 100%; width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Sifat-Sifat%20Logaritma.jpg" alt="Sifat-Sifat Logaritma" width="600" height="600" /></p>
<p> </p>
<p><em>“Duh, kenapa banyak banget sih sifat-sifat logaritma itu? Males ih ngafalinnya. Ribet!”</em></p>
<p style="text-align: justify;"><em>Eits</em>… jangan salah, semua sifat di atas pasti bisa kamu kuasai dengan mudah, <em>kok</em>. Caranya, kamu bisa memperbanyak latihan soal tentang logaritma. Tentunya, di aplikasi <strong>Ruangguru</strong>, dong. <em>Hehehe</em>…</p>
<p><strong>Baca Juga: <a href="/blog/persamaan-logaritma-mtk-kelas-x" rel="noopener">Bentuk-Bentuk Persamaan Logaritma dan Cara Menyelesaikannya</a></strong></p>
<p style="text-align: justify;">Oke, supaya kamu jadi paham sifat-sifat logaritma di atas dipakai untuk model soal seperti apa, ayo kita coba kerjakan soal di bawah ini. Kita kerjakan bersama-sama, ya!</p>
<p style="text-align: center;">—</p>
<p style="text-align: justify;">Gimana, kamu sudah cukup paham tentang materi logaritma? Sebelum lanjut ke contoh-contoh soal logaritma, misalnya kamu mau mempelajari materi logaritma bareng ahlinya, boleh banget gabung di <strong><a href="https://www.ruangguru.com/privat/matematika">Ruangguru Privat Matematika</a></strong>.</p>
<p style="text-align: justify;">Di Ruangguru Privat, kamu akan dimentori oleh guru-guru berkualitas yang sudah terstandarisasi. Kamu juga bebas mau pilih belajar secara tatap muka (<em>offline</em>) atau lewat daring (<em>online</em>). Fleksibel banget, kan. Yuk langsung daftar sekarang!</p>
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<p> </p>
<h2><span style="font-size: 18pt;">Contoh Soal Logaritma dan Pembahasannya</span></h2>
<p>Sekarang, kita coba kerjakan contoh soal logaritma, ya! Perhatikan soal berikut:</p>
<p><img decoding="async" style="height: auto; max-width: 100%; width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Contoh%20Soal%20Logaritma.jpg" alt="Contoh Soal Logaritma" /></p>
<p> </p>
<p><strong>Pembahasan:</strong></p>
<p><strong><span style="background-color: transparent;">Soal 1</span></strong></p>
<p style="text-align: justify;"><span style="background-color: transparent;">Pada soal nomor 1, hal pertama yang harus kita lakukan adalah </span><strong style="background-color: transparent;">cek basisnya</strong><span style="background-color: transparent;">. Kedua persamaan logaritma di atas, ternyata memiliki nilai basis yang sama, yaitu 2. </span></p>
<p style="text-align: justify;"><span style="background-color: transparent;"><em>Nah</em>, karena basisnya sama, kita bisa menggunakan sifat logaritma yang kedua <em>nih, </em>untuk mengetahui hasilnya. Sehingga, </span><sup style="background-color: transparent;">2</sup><span style="background-color: transparent;">log 4 + </span><sup style="background-color: transparent;">2</sup><span style="background-color: transparent;">log 8 = </span><sup style="background-color: transparent;">2</sup><span style="background-color: transparent;">log (4 × 8) = </span><sup style="background-color: transparent;">2</sup><span style="background-color: transparent;">log 32 = 5. </span></p>
<p style="text-align: justify;"><span style="background-color: transparent;"><strong>Ingat!</strong> tujuan logaritma adalah mencari pangkat. Jadi, 2 pangkat berapa yang hasilnya 32? <strong>Jawabannya adalah 5</strong>. </span><span style="background-color: transparent;">Mudah, ya? Kita lanjut ke soal nomor 2, </span><em style="background-color: transparent;">yuk</em><span style="background-color: transparent;">!</span></p>
<p> </p>
<p><strong>Soal 2</strong></p>
<p style="text-align: justify;"><span style="background-color: transparent;">Pada soal nomor 2 ini, kita tidak bisa langsung mengerjakannya karena kamu pasti akan bingung untuk mencari nilai pangkat dari 8 yang hasilnya 32. Lalu bagaimana? </span></p>
<p style="text-align: justify;"><span style="background-color: transparent;">Kalau kita perhatikan soalnya dengan jeli, 8 itu merupakan hasil pemangkatan dari 2</span><sup style="background-color: transparent;">3</sup><span style="background-color: transparent;"> dan 32 merupakan hasil pemangkatan dari 2</span><sup style="background-color: transparent;">5</sup><span style="background-color: transparent;">. Sehingga, bentuk logaritmanya <span style="font-weight: bold;">bisa kita ubah</span> menjadi seperti berikut:</span></p>
<p><span style="background-color: transparent;"><img decoding="async" style="width: 381px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/logaritma%2011.png" alt="logaritma dan sifat-sifatnya" width="381" /></span></p>
<p> </p>
<p><strong>Soal 3</strong></p>
<p style="text-align: justify;">Gimana? sudah mulai greget? <em>Nah</em>, soal nomor 3 ini akan membuat kamu semakin gregetan lagi, nih! Perlu kamu ketahui, model soal nomor 3 akan sering kamu temui pada soal-soal ujian maupun soal-soal seleksi Perguruan Tinggi, <em style="font-size: 16px;">lho</em><span style="font-size: 16px;">. </span></p>
<p style="text-align: justify;"><span style="font-size: 16px;">Kelihatannya memang cukup rumit ya, tapi jika kamu telah paham konsepnya, soal ini akan jadi sangat mudah untuk dikerjakan. Jika kamu menemui model soal seperti ini, kamu bisa menyelesaikannya menggunakan sifat logaritma nomor 4. </span></p>
<p style="text-align: justify;"><span style="font-size: 16px;">Sehingga, pengerjaannya akan menjadi seperti berikut:</span></p>
<p><img decoding="async" style="width: 297px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/logaritma%2022.png" alt="logaritma dan sifat-sifatnya" width="297" /></p>
<p> </p>
<p><strong><em>Note</em>: </strong>Untuk memilih basis, kita lihat saja angka yang paling sering muncul pada soal. Angka 2 muncul sebanyak 2 kali, 8 sebanyak 1 kali, dan 7 sebanyak 1 kali. Angka yang paling banyak muncul adalah 2, sehingga kita pilih 2 sebagai basis. Paham, ya?</p>
<p style="text-align: justify;"><img decoding="async" style="width: 145px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/logaritma%2031.png" alt="logaritma dan sifat-sifatnya" width="145" /></p>
<p style="text-align: justify;">Selanjutnya, kita <strong>uraikan numerusnya</strong>. Usahakan kita ubah kebentuk yang sudah ada pada soal. Maksudnya gimana? Begini, di soal diketahui <sup>2</sup>log <span style="color: #ff0201;">8</span> dan <sup>2</sup>log <span style="color: #ff0201;">7</span>. Karena numerusnya 8 dan 7, kita uraikan 14 menjadi <span style="color: #ff0201;">7</span> × 2 dan 16 menjadi <span style="color: #ff0201;">8</span> × 2 agar kita bisa ketahui hasil akhirnya.</p>
<p><img decoding="async" style="width: 378px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/logaritma%2041.png" alt="logaritma dan sifat-sifatnya" width="378" /></p>
<p><strong>Baca Juga: <a href="/blog/fungsi-komposisi" rel="noopener">Belajar Fungsi Komposisi & Contohnya, Lengkap!</a></strong></p>
<p style="text-align: justify;">Setelah kamu memahami ketiga contoh soal di atas, bagaimana menurutmu? Ternyata logaritma bukanlah materi yang sulit untuk dipahami, ya.</p>
<p style="text-align: justify;">Kamu juga perlu ingat <em>nih</em>, karena tujuan logaritma adalah mencari pangkat, maka modal pertama yang harus kamu miliki adalah <span style="font-weight: bold;">hafal perkalian</span>. Setelah itu, kamu juga harus paham dengan sifat-sifat logaritma. Jangan lupa untuk perbanyak latihan soal agar kamu semakin mantap lagi, <em>nih</em>.</p>
<p style="text-align: justify;">Oh ya, di bawah ini ada latihan soal yang bisa kamu kerjakan. Bagi yang tahu, jangan ragu untuk tulis jawabanmu di kolom komentar ya!</p>
<p><img decoding="async" style="height: auto; max-width: 100%; width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Latihan%20Soal%20Logaritma.jpg" alt="Latihan Soal Logaritma" width="600" height="400" /></p>
<p> </p>
<p style="text-align: justify;">Wah, menarik ya pembahasan kali ini. Bagi kamu yang masih kurang paham, kamu bisa lho, belajar lebih lanjut di <strong><a href="https://www.ruangguru.com/ruangbelajar" target="_blank" rel="noopener">ruangbelajar</a></strong>. Belajar jadi mudah dan praktis di mana saja dan kapan saja. Yuk, buruan <em>download</em> aplikasinya sekarang!</p>
<p><a href="https://www.ruangguru.com/ruangbelajar"><img decoding="async" class="aligncenter size-medium" src="https://cdn-web-2.ruangguru.com/landing-pages/assets/a2dbab8e-e903-4b70-ae04-39ff5807647e.jpg" alt="CTA ruangbelajar" width="820" /></a></p>
<p style="text-align: justify;"><strong>Referensi:</strong></p>
<p style="text-align: left;">Sinaga, B. Sinambela, P. N. J. M. Sitanggang, A. K. dkk. (2014). <em>Matematika</em>. Jakarta: Kemendikbud.</p>
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<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">
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</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>
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</a>
</li>
<li>
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<img src="https://cdn-web-2.ruangguru.com/static/googleplay.png" loading="lazy" alt="Button Google Play Footer " />
</a>
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<img src="https://cdn-web-2.ruangguru.com/static/huawei.png" loading="lazy" alt="Button AppGallery Footer " />
</a>
</li>
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</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>
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<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>
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</picture>
</a>
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<picture>
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</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>
<meta name="author" content="Ruangguru Tech Team">
<!-- Google Tag Manager (noscript) -->
<noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PVNLZFT" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
<!-- Tracker -->
<script type="text/javascript" src="https://cdn-web-2.ruangguru.com/landing-page-web/public/staticpages/global-assets/js/cta.js"></script>
<script src="https://unpkg.com/@dotlottie/player-component@latest/dist/dotlottie-player.mjs" type="module"></script>
</body>
</html>