{"id":312322,"date":"2023-02-07T14:48:00","date_gmt":"2023-02-07T07:48:00","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=312322"},"modified":"2023-02-08T11:06:58","modified_gmt":"2023-02-08T04:06:58","slug":"persamaan-eksponen","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/persamaan-eksponen\/","title":{"rendered":"Pengertian Persamaan Eksponen, Sifat dan Contoh Soalnya"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1280\" height=\"853\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/pexels-karolina-grabowska-5238081-1.webp\" alt=\"\" class=\"wp-image-312329\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/pexels-karolina-grabowska-5238081-1.webp 1280w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/pexels-karolina-grabowska-5238081-1-768x512.webp 768w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/pexels-karolina-grabowska-5238081-1-1200x800.webp 1200w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/pexels-karolina-grabowska-5238081-1-1170x780.webp 1170w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/pexels-karolina-grabowska-5238081-1-585x390.webp?crop=1 585w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/pexels-karolina-grabowska-5238081-1-263x175.webp?crop=1 263w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Hai Quipperian, saat di SD kamu sudah mengenal istilah bilangan berpangkat, kan? Tahukah kamu jika bilangan berpangkat merupakan dasar yang harus kamu kuasai saat belajar persamaan eksponen, <em>lho<\/em>. Lalu, apa yang dimaksud persamaan eksponen itu? Untuk tahu pembahasannya, yuk simak artikel berikut ini.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Pengertian Persamaan Eksponen<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Di artikel sebelumnya, Quipper Blog sudah pernah membahas apa itu eksponen. Eksponen merupakan bentuk perkalian suatu bilangan dengan dirinya sendiri sebanyak pangkatnya. Persamaan eksponen adalah persamaan bilangan berpangkat yang memuat variabel di bagian pangkatnya. Oleh karena memuat suatu variabel, maka pangkatnya bisa dinyatakan sebagai suatu fungsi, misal <em>f<\/em>(<em>x<\/em>) atau g(<em>x<\/em>) untuk pangkat bervariabel <em>x<\/em>. Contoh persamaan eksponen adalah 3<sup>2<\/sup><em><sup>x<\/sup><\/em><sup> \u2013 4 <\/sup>&nbsp;= 3<sup>2<\/sup>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Bentuk Umum Persamaan Eksponen<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Adapun bentuk umum persamaan eksponen adalah sebagai berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>a<\/em><em><sup>f(x)<\/sup><\/em><sup> <\/sup>= <em>a<\/em><em><sup>g<\/sup><\/em><sup>(<\/sup><em><sup>x<\/sup><\/em><sup>)<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>a<\/em> = basis (bilangan pokok); dan<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>f<\/em>(<em>x<\/em>) dan <em>g<\/em>(<em>x<\/em>) = pangkat atau eksponen.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Quipperian harus ingat ya, jika bentuk umum persamaan eksponen pasti memuat variabel di bagian pangkatnya. Jika variabel bukan di bagian pangkat, maka persamaannya bukan termasuk persamaan eksponen, contoh:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2<em><sup>x<\/sup><\/em><sup> + 1<\/sup> = 2<sup>5<\/sup> \u2192 persamaan eksponen<\/li>\n\n\n\n<li>(2<em>x<\/em> + 1)<sup>2<\/sup><em><sup>x<\/sup><\/em> = <em>x<\/em><sup>x \u2013 1&nbsp; <\/sup>&nbsp;\u2192 persamaan eksponen<\/li>\n\n\n\n<li><em>x<\/em><sup>2<\/sup> + 2 = 0<sup>&nbsp; <\/sup>\u2192 bukan persamaan eksponen karena variabelnya terletak di bagian basis.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Meskipun memiliki bentuk umum tertentu, namun persamaan eksponen itu beragam seperti persamaan eksponen bentuk akar, persamaan eksponen sederhana, persamaan eksponen tak sederhana, dan lainnya.<\/p>\n\n\n\n<div class=\"baca\">\n<p><span class=\"head_baca\">Baca Juga: <\/span> <a href=\"https:\/\/www.quipper.com\/id\/blog\/mapel\/matematika\/pertidaksamaan-eksponen\/\">Pengertian Pertidaksamaan Eksponen dengan Contohnya<\/a><\/p>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Sifat-Sifat Persamaan Eksponen<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Meskipun memiliki bentuk umum tertentu, namun pengembangan persamaan eksponen bisa bervariasi. Untuk memudahkanmu dalam menyelesaikan permasalahan terkait persamaan eksponen, gunakan sifat-sifat berikut ini.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Untuk <em>a<\/em><em><sup>f<\/sup><\/em><sup>(<\/sup><em><sup>x<\/sup><\/em><sup>)<\/sup> = <em>a<\/em><em><sup>k<\/sup><\/em> dengan <em>a<\/em> &gt; 0 dan <em>a<\/em> \u2260 1, berlaku <em>f<\/em>(<em>x<\/em>) = <em>k<\/em><\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Jika basisnya sama, maka nilai pangkat basis pertama akan sama dengan pangkat basis kedua. Perhatikan contoh berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2<em><sup>x<\/sup><\/em><sup> + 1<\/sup> = 2<sup>4<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>x<\/em> + 1 = 4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>x<\/em> = 3<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>Untuk <em>a<\/em><em><sup>f<\/sup><\/em><sup>(<\/sup><em><sup>x<\/sup><\/em><sup>)<\/sup> = <em>a<\/em><em><sup>g<\/sup><\/em><sup>(<\/sup><em><sup>x<\/sup><\/em><sup>)<\/sup> dengan <em>a<\/em> &gt; 0 dan <em>a<\/em> <strong>\u2260 <\/strong>1, berlaku <em>f<\/em>(<em>x<\/em>) = <em>g<\/em>(<em>x<\/em>)<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Pada dasarnya, sifat kedua ini sama dengan sifat pertama. Hanya saja, kedua pangkatnya berupa fungsi <em>x<\/em>.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li><em>a<\/em><em><sup>f<\/sup><\/em><sup>(<\/sup><em><sup>x<\/sup><\/em><sup>)<\/sup> = <em>b<\/em><em><sup>f<\/sup><\/em><sup>(<\/sup><em><sup>x<\/sup><\/em><sup>)<\/sup> dengan <em>a<\/em> &gt; 0, <em>a<\/em> \u2260 1, <em>b<\/em> &gt; 0, dan <em>b<\/em> \u2260 1 berlaku <em>f<\/em>(<em>x<\/em>) = 0<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">sifat ketiga ini berlaku jika basisnya tidak sama, namun bentuk eksponennya sama. Perhatikan contoh berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">4<em><sup>2x<\/sup><\/em><sup> + 3<\/sup> = 5<em><sup>2x<\/sup><\/em><sup> + 3<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2<em>x<\/em> + 3 = 0<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n<li><em>a<\/em><em><sup>f<\/sup><\/em><sup>(<\/sup><em><sup>x<\/sup><\/em><sup>)<\/sup> = <em>b<\/em><em><sup>g<\/sup><\/em><sup>(<\/sup><em><sup>x<\/sup><\/em><sup>)<\/sup> \u2192 penyelesaian dengan sistem logaritma<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">sifat keempat ini berlaku jika basis dan pangkat keduanya tidak sama. Untuk menentukan nilai variabelnya, kamu bisa menggunakan sistem logaritma. Perhatikan contoh berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2<em><sup>x<\/sup><\/em><sup> + 1<\/sup> = 3<em><sup>x<\/sup><\/em><sup> &#8211; 2<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">log2<em><sup>x<\/sup><\/em><sup> + 1<\/sup> = log 3<em><sup>x<\/sup><\/em><sup> &#8211; 2<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(<em>x<\/em> + 1) log2 = (<em>x<\/em> &#8211; 2) log3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>x<\/em> log2 + log2 = <em>x<\/em>log3 &#8211; 2log3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">3log3 = <em>x<\/em>log3 \u2013 <em>x<\/em>log2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>x<\/em>log3 \u2013 <em>x<\/em>log2 = 3log3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>x<\/em> log 3 log 2 = 3 log3 \u2192 ingat, <em>a<\/em>log<em>a<\/em> = 1, sehingga<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>x<\/em> = log 2 log 3<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Langkah-Langkah Menyelesaikan Persamaan Eksponen<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Jika basis kedua eksponen sama, tentu kamu bisa dengan mudah menyelesaikannya. Namun, bagaimana jika basisnya tidak sama? Untuk itu langkah-langkah menyelesaikan persamaan eksponen dengan basis berbeda adalah sebagai berikut.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Identifikasi Dahulu Kedua Basisnya<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Langkah pertama adalah kamu harus mengidentifikasi basis dari kedua eksponen. Maksudnya, apakah basisnya bisa disamakan atau tidak. Jika bisa disamakan, uraikan kedua bentuk eksponen dalam bentuk basis (bilangan pokok) yang sama. Namun, jika tidak bisa disamakan, gunakan persamaan logaritma. Misal:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2<sup>2<\/sup><em><sup>x<\/sup><\/em> = 8<em><sup>x<\/sup><\/em><sup>+1<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Persamaan di atas memiliki basis yang tidak sama, kan? Basis pertama 2 dan basis keduanya 8. Tapi kamu harus ingat bahwa 8 bisa dijadikan bilangan berpangkat dengan basis 2, yaitu 2<sup>3<\/sup>, sehingga persamaannya menjadi:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2<sup>2<\/sup><em><sup>x<\/sup><\/em> = 2<sup>3<\/sup><em><sup>x<\/sup><\/em><sup> + 3<\/sup><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Operasikan Pangkat Sesuai Sifat-Sifat Persamaan Eksponen<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Setelah identifikasi selesai, kamu bisa menyelesaikan operasi pangkatnya sesuai sifat-sifat persamaan eksponen yang ada, sehingga bisa diperoleh nilai variabel pangkatnya sebagai solusi dari persamaan yang dimaksud.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2<sup>2<\/sup><em><sup>x<\/sup><\/em> = 2<sup>3<\/sup><em><sup>x<\/sup><\/em><sup> + 3<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Oleh karena basisnya sudah sama, maka:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2<em>x<\/em> = 3<em>x<\/em> + 3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>x<\/em> = -3<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Substitusikan Nilai Variabel yang Diperoleh pada Persamaan<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Langkah ketiga ini bertujuan untuk menguji kebenaran dari nilai variabel yang kamu dapatkan. Jika kedua persamaan itu hasilnya sama, maka nilai variabelnya benar.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Substitusikan nilai <em>x<\/em> = -3 pada persamaan awalnya.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2<sup>2<\/sup><em><sup>x<\/sup><\/em> = 8<em><sup>x<\/sup><\/em><sup>+1<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2<sup>2(-3)<\/sup> = 8<sup>(-3 + 1)<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2<sup>-6<\/sup> = 8<sup>-2<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">0,015625 = 0,015625 (hasilnya sama)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan demikian, <em>x<\/em> = -3 adalah benar.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Contoh Soal Persamaan Eksponen<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk mengasah pemahamanmu, yuk simak beberapa contoh soal berikut.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Contoh Soal 1<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui <em>p<\/em> dan <em>q<\/em> merupakan bilangan bulat yang bisa memenuhi persamaan <sub><\/sub>. Berapakah nilai <em>p<\/em><sup>2<\/sup> + <em>q<\/em><sup>2<\/sup>?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mula-mula, kamu harus mencari masing-masing nilai <em>p<\/em> dan <em>q<\/em>.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/ygOcD3KuyJkK03RCmnbdP_rvGe3mT4OtwLJ02lyIn6E7gZDOY5yCDOcogoZ4cpkgIo6nJknwUeJT-W6D1P6DmrvupEhQqg9IMrgwZn_SySqSX5c76tluPBuM7t19SKWctEnmTFb4-RkaSI8ODwbxHA\" alt=\"\" width=\"114\" height=\"129\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan demikian, nilai <em>p<\/em><sup>2<\/sup> + <em>q<\/em><sup>2<\/sup> adalah (2)<sup>2<\/sup> + (-3)<sup>2<\/sup> = 4 + 9 = 13.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, nilai <em>p<\/em><sup>2<\/sup> + <em>q<\/em><sup>2<\/sup> = 13.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Contoh Soal 2<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Jika <sub><\/sub>, tentukan nilai <em>b<\/em> (dalam <em>p<\/em>) yang memenuhi persamaan berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/CNjdRrhylSXPFG8VDymCzqs49DP7_b361KH0Er__pSErApwvSCt1XvFiNQJ4vMSqNp91u4GWwuuiiLNmXzv5MIa6V54JU_ONDvk_vX01Q71x8Si7r5uPA29ewYQsnA6ze7XIPhiVVLL8zUsUare1cg\" alt=\"\" width=\"88\" height=\"43\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Gunakan cara seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/_i98dYbm_HCn2ZUojMckXSF7fqh-_rEZZVapjuJlEtWO3jIOK0R0xSOW8icm_efWUKB4_g0HD1Xtdy4s05eSzK_WLol-fS4THjYZxBw980LdTQT4EhQbRgwQkTGjyX5B648CsBCQ8TfzRgz-GBb31A\" alt=\"\" width=\"280\" height=\"230\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, nilai <em>b<\/em> (dalam <em>p<\/em>) yang memenuhi persamaan tersebut adalah <em>b<\/em> = 1 \u2013 <em>p<\/em>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Contoh Soal 3<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Tentukan solusi <em>x<\/em> dari persamaan berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/155eR-cNiKLOU-pvDmu33nKFcJ_YBiYKwltBajPxHDL0m8-UtBxJfBW1xeEWPb3it6CHftq2pTZ28erR1pla85Pxgb2EUq9tZNve8VJ2tjqqGQLdUf6-BoEoQC3pBEr2b2ex_mpnECoH9slKHuUqCA\" alt=\"\" width=\"91\" height=\"23\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Solusinya adalah sebagai berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/n0n9OO9yIFtc5tshZ_ihL7X5wfbZPHer9Nh_44bIhu2SCmq-9WKf6-wGxVuYo7AAKLWNH6bIiEjmvYcEmAybYg4cs7qsILBP370q1nwItbZ70AoKIL-WyWIoYkAmVbFeMSHIT1yFMedTQJ3Pa-g67A\" alt=\"\" width=\"129\" height=\"147\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, nilai <em>x<\/em> yang memenuhi persamaan tersebut adalah <sub><\/sub>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sampai sini, apakah Quipperian sudah paham tentang persamaan eksponen? Agar cepat paham, sering-sering kerjakan latihan soal ya.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Itulah pembahasan Quipper Blog kali ini. Semoga bermanfaat. Untuk mendapatkan materi lengkapnya, yuk buruan gabung Quipper Video. Salam Quipper!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hai Quipperian, saat di SD kamu sudah mengenal istilah bilangan berpangkat, kan? Tahukah kamu jika bilangan berpangkat merupakan dasar yang harus kamu kuasai saat&hellip;<\/p>\n","protected":false},"author":156447303,"featured_media":312329,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[679384865],"tags":[679386731],"ppma_author":[679386823],"class_list":["post-312322","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika","tag-materi-matematika-kelas-10"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Pengertian Persamaan Eksponen, Sifat dan Contoh Soalnya - Quipper Blog<\/title>\n<meta name=\"description\" content=\"Persamaan eksponen adalah persamaan bilangan berpangkat yang memuat variabel di bagian pangkatnya. 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