{"id":277878,"date":"2019-12-12T12:59:59","date_gmt":"2019-12-12T05:59:59","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=277878"},"modified":"2023-02-07T15:25:40","modified_gmt":"2023-02-07T08:25:40","slug":"eksponen-matematika-matematika-kelas-10","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/eksponen-matematika-matematika-kelas-10\/","title":{"rendered":"Eksponen Matematika &#8211; Matematika Kelas 10"},"content":{"rendered":"<p><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-277910\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-d.png\" alt=\"\" width=\"800\" height=\"533\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-d.png 800w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-d-768x512.png 768w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-d-585x390.png?crop=1 585w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-d-263x175.png?crop=1 263w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-d-300x200.png 300w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Hai Quipperian, bagaimana kabarnya? Semoga selalu sehat dan tetap semangat, ya!<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Pernahkah kamu mendengar istilah sensus penduduk? Sensus penduduk adalah proses yang dilakukan pemerintah untuk mengetahui jumlah penduduk dalam selang waktu tertentu, biasanya 10 tahun sekali. Dari data yang diperoleh setiap 10 tahun sekali itu, pemerintah bisa menghitung pertumbuhan penduduk untuk beberapa tahun selanjutnya. Perhitungan itu tentu bersifat pendekatan atau perkiraan saja. Apakah bisa demikian? Tentu bisa dengan menggunakan pendekatan secara eksponen. Apakah itu eksponen? Temukan jawabannya di pembahasan Quipper Blog kali ini. <\/span><i><span style=\"font-weight: 400;\">Check this out<\/span><\/i><span style=\"font-weight: 400;\">!<\/span><\/p>\n<h2><b>Pengertian Eksponen<\/b><\/h2>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-277913\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-a.png\" alt=\"\" width=\"800\" height=\"533\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-a.png 800w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-a-300x200.png 300w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-a-768x512.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Eksponen adalah bentuk perkalian suatu bilangan yang sama secara berulang-ulang. Mungkin Quipperian biasa mendengar istilahnya sebagai bilangan berpangkat. Contohnya sebagai berikut.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"> <img decoding=\"async\" class=\"alignnone size-full wp-image-277904\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-1.png\" alt=\"\" width=\"177\" height=\"71\"><\/span><\/p>\n<p><span style=\"font-weight: 400;\">Bentuk eksponen bisa dinyatakan dalam bentuk persamaan maupun pertidaksamaan. Hal itu berkaitan dengan jenis penggunaannya, misalnya untuk menyelesaikan masalah yang berkaitan dengan fungsi eksponen. Nah, konsep dasar perkalian berulang-ulang inilah yang nantinya digunakan pemerintah untuk menghitung jumlah penduduk beberapa tahun ke depan. Tentunya dengan perhitungan dan penurunan rumus yang tidak mudah, ya!<\/span><\/p>\n<h2><b>Persamaan Eksponen<\/b><\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-277912\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-b.png\" alt=\"\" width=\"800\" height=\"533\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-b.png 800w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-b-300x200.png 300w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-b-768x512.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Persamaan eksponen adalah persamaan yang memiliki variabel di bagian eksponennya. Secara umum, persamaan eksponen dibagi menjadi tiga, yaitu persamaan eksponen berbasis konstanta, persamaan eksponen berbasis fungsi, dan persamaan eksponen dalam bentuk penjumlahan. Untuk penjelasan lebih lengkapnya, simak ulasan berikut.<\/span><\/p>\n<h3><b>1. Persamaan eksponen berbasis konstanta<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Untuk persamaan eksponen berbasis konstanta, terdapat dua persamaan yang harus Quipperian pahami, yaitu sebagai berikut.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-277903\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-2.png\" alt=\"\" width=\"439\" height=\"93\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-2.png 439w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-2-300x64.png 300w\" sizes=\"(max-width: 439px) 100vw, 439px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Untuk lebih jelasnya, simak contoh soal berikut ini.<\/span><\/p>\n<h4><b>Contoh Soal 1<\/b><\/h4>\n<p><span style=\"font-weight: 400;\">Tentukan solusi dari persamaan <\/span>3<sup>x+2<\/sup> = 9<sup>x-2<\/sup>!<\/p>\n<p><b>Pembahasan:<\/b><\/p>\n<p><span style=\"font-weight: 400;\">Untuk menentukan solusinya, Quipperian harus menyamakan basis kedua ruas terlebih dahulu. Berdasarkan sifat-sifat eksponen, diperoleh:<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-277902\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-3.png\" alt=\"\" width=\"408\" height=\"180\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-3.png 408w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-3-300x132.png 300w\" sizes=\"(max-width: 408px) 100vw, 408px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Jadi, solusi dari persamaan 3<sup>x+2<\/sup> = 9<sup>x-2 <\/sup><\/span><span style=\"font-weight: 400;\">adalah <\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\"> = 6.<\/span><\/p>\n<h3><b>2. Persamaan eksponen berbasis fungsi<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Bentuk umum persamaan eksponen berbasis fungsi adalah sebagai berikut.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-277901\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-4.png\" alt=\"\" width=\"167\" height=\"66\">&nbsp;<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Bentuk persamaan eksponen di atas memiliki empat kemungkinan solusi, yaitu sebagai berikut.<\/span><\/p>\n<ol>\n<li style=\"font-weight: 400;\"><i><span style=\"font-weight: 400;\">g<\/span><\/i><span style=\"font-weight: 400;\">(<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">) = <\/span><i><span style=\"font-weight: 400;\">h<\/span><\/i><span style=\"font-weight: 400;\">(<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">)<\/span><\/li>\n<li style=\"font-weight: 400;\"><i><span style=\"font-weight: 400;\">f<\/span><\/i><span style=\"font-weight: 400;\">(<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">) = 1<\/span><\/li>\n<li style=\"font-weight: 400;\"><i><span style=\"font-weight: 400;\">f<\/span><\/i><span style=\"font-weight: 400;\">(<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">) = -1, dengan syarat <\/span><i><span style=\"font-weight: 400;\">g<\/span><\/i><span style=\"font-weight: 400;\">(<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">) dan <\/span><i><span style=\"font-weight: 400;\">h<\/span><\/i><span style=\"font-weight: 400;\">(<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">) sama-sama genap atau ganjil.<\/span><\/li>\n<li style=\"font-weight: 400;\"><i><span style=\"font-weight: 400;\">f<\/span><\/i><span style=\"font-weight: 400;\"> (<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">) = 0, dengan syarat <\/span><i><span style=\"font-weight: 400;\">g<\/span><\/i><span style=\"font-weight: 400;\">(<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">), <\/span><i><span style=\"font-weight: 400;\">h<\/span><\/i><span style=\"font-weight: 400;\">(<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">) &gt; 0.<\/span><\/li>\n<\/ol>\n<p><span style=\"font-weight: 400;\">Untuk mengetahui penerapan persamaan eksponen berbasis fungsi pada soal, simak contoh berikut.<\/span><\/p>\n<h4><b>Contoh Soal 2<\/b><\/h4>\n<p><span style=\"font-weight: 400;\">Tentukan himpunan penyelesaian dari persamaan eksponen&nbsp;<\/span>(x &#8211; 2)<sup>x<sup>2<\/sup>-2x<\/sup> = (x &#8211; 2)<sup>x+4<\/sup>!<\/p>\n<p><b>Pembahasan:<\/b><\/p>\n<p><span style=\"font-weight: 400;\">Solusi dari persamaan eksponen di atas didapat dari 4 kondisi berikut.<\/span><\/p>\n<p><b>a. Solusi ke-1<\/b><\/p>\n<p><span style=\"font-weight: 400;\"> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-277899\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-6.png\" alt=\"\" width=\"155\" height=\"118\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-6.png 155w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-6-80x60.png 80w\" sizes=\"(max-width: 155px) 100vw, 155px\" \/><\/span><\/p>\n<p><b>b. Solusi ke-2<\/b><\/p>\n<p><span style=\"font-weight: 400;\"> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-277898\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-7.png\" alt=\"\" width=\"91\" height=\"62\"><\/span><\/p>\n<p><b>c. Solusi ke-3<\/b><\/p>\n<p><span style=\"font-weight: 400;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-277897\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-8.png\" alt=\"\" width=\"96\" height=\"62\">&nbsp;<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Sekarang Quipperian periksa apakah <\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\"> = 1, <\/span><i><span style=\"font-weight: 400;\">g<\/span><\/i><span style=\"font-weight: 400;\">(<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">) dan <\/span><i><span style=\"font-weight: 400;\">h<\/span><\/i><span style=\"font-weight: 400;\">(<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">) sama-sama genap atau sama-sama ganjil.<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Uji pangkat untuk ruas kiri.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\"> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-277896\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-9.png\" alt=\"\" width=\"235\" height=\"44\"><\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Uji pangkat untuk ruas kanan<\/span><\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-277895\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-10.png\" alt=\"\" width=\"187\" height=\"44\"><\/p>\n<p><span style=\"font-weight: 400;\">Oleh karena sama-sama ganjil, maka <\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\"> = 1 merupakan penyelesaian.&nbsp;<\/span><\/p>\n<p><b>d. Solusi ke-4<\/b><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-277894\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-11.png\" alt=\"\" width=\"109\" height=\"64\"><\/p>\n<p><span style=\"font-weight: 400;\">Cobalah periksa, apakah untuk <\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\"> = 2, <\/span><i><span style=\"font-weight: 400;\">g<\/span><\/i><span style=\"font-weight: 400;\">(<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">) dan <\/span><i><span style=\"font-weight: 400;\">h<\/span><\/i><span style=\"font-weight: 400;\">(<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">) sama-sama bernilai positif?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Uji pangkat ruas kiri menunjukkan bahwa:<\/span><\/p>\n<p><em><span style=\"font-weight: 400;\">x<sup>2<\/sup> &#8211; 2x = 2<sup>2<\/sup> &#8211; 2(2) = 0&nbsp;<\/span><\/em><\/p>\n<p><span style=\"font-weight: 400;\">Oleh karena 0 bukan bilangan positif, maka <\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\"> = 2 bukan termasuk penyelesaian.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Jadi, himpunan penyelesaian dari persamaan eksponen di atas <\/span><span style=\"font-weight: 400;\">adalah {-1, 1, 3, 4}.<\/span><\/p>\n<h3><b>3. Persamaan eksponen berbentuk penjumlahan<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Bentuk umum persamaan eksponen penjumlahan adalah sebagai berikut.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-277891\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-14.png\" alt=\"\" width=\"326\" height=\"66\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-14.png 326w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-14-300x61.png 300w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><\/span><\/p>\n<p><span style=\"font-weight: 400;\">Lalu, bagaimana langkah-langkah menentukan hasil persamaan eksponen berbentuk penjumlahan ini? check this out!<\/span><\/p>\n<p><span style=\"font-weight: 400;\">a. Bentuk eksponen harus diuraikan sampai diperoleh bentuk yang sama. Untuk menguraikannya, gunakan sifat-sifat berikut.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-277890\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-15.png\" alt=\"\" width=\"164\" height=\"111\"><\/p>\n<p><span style=\"font-weight: 400;\">b. Gunakan permisalan bentuk eksponen yang sama dengan variabel tertentu.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">c. Selesaikan persamaannya, lalu substitusikan kembali nilai variabel yang diperoleh pada permisalan.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Untuk lebih jelasnya, simak contoh soal berikut ini.<\/span><\/p>\n<h4><b>Contoh Soal 3<\/b><\/h4>\n<p><span style=\"font-weight: 400;\">Tentukan solusi dari persamaan eksponen <\/span>2<sup>x+1<\/sup> + 2<sup>x-1<\/sup> = 20<span style=\"font-weight: 400;\">!<\/span><\/p>\n<p><b>Pembahasan:<\/b><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-277889\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-16.png\" alt=\"\" width=\"175\" height=\"114\"><\/p>\n<p><span style=\"font-weight: 400;\">Misalkan, 2<\/span><sup>x <\/sup><span style=\"font-weight: 400;\">= <\/span><i><span style=\"font-weight: 400;\">y<\/span><\/i><span style=\"font-weight: 400;\">, sehingga diperoleh:<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-277888\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-17.png\" alt=\"\" width=\"116\" height=\"94\">&nbsp;<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Substitusikan nilai balik <\/span><i><span style=\"font-weight: 400;\">y<\/span><\/i><span style=\"font-weight: 400;\"> pada permisalan tersebut.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-277887\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-18.png\" alt=\"\" width=\"124\" height=\"133\"><\/span><\/p>\n<p><span style=\"font-weight: 400;\">Jadi, solusi dari persamaan eksponen 2<sup>x+1<\/sup> + 2<sup>x-1<\/sup> = 20<\/span><span style=\"font-weight: 400;\">&nbsp;adalah <\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\"> = 3.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Bagaimana Quipperian, mudah bukan belajar persamaan eksponen? Nah, setelah persamaan eksponen, Quipper Blog akan mengajak Quipperian untuk belajar tentang pertidaksamaan eksponen. Seperti apa ulasannya?<\/span><\/p>\n<h2><b>Pertidaksamaan Eksponen<\/b><\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-277911\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-c.png\" alt=\"\" width=\"800\" height=\"533\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-c.png 800w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-c-300x200.png 300w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-c-768x512.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Pertidaksamaan eksponen adalah pertidaksamaan jenis eksponen yang memiliki variabel. Ternyata, pertidaksamaan eksponen memiliki dua bentuk umum <\/span><i><span style=\"font-weight: 400;\">lho<\/span><\/i><span style=\"font-weight: 400;\">, yaitu sebagai berikut.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-277886\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-19.png\" alt=\"\" width=\"333\" height=\"69\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-19.png 333w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-19-300x62.png 300w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-19-326x69.png 326w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Untuk menentukan solusi pertidaksamaan eksponen seperti pertidaksamaan di atas, ikuti langkah berikut.<\/span><\/p>\n<ol>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Bentuk eksponen harus diuraikan sampai diperoleh bentuk yang sama. Uraikan berdasarkan sifat-sifat eksponen.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Gunakan permisalan bentuk eksponen dengan variabel tertentu.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Selesaikan pertidaksamaannya menggunakan konsep pertidaksamaan sampai diperoleh interval untuk permisalannya.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Susbtitusikan nilai balik yang diperoleh pada permisalan.<\/span><\/li>\n<\/ol>\n<p><span style=\"font-weight: 400;\">Agar Quipperian tambah paham dengan pertidaksamaan eksponen, perhatikan contoh berikut.<\/span><\/p>\n<h3><b>Contoh Soal 4<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Tentukan himpunan penyelesaian dari pertidaksamaan eksponen <\/span>49<sup>3x-4<\/sup> &gt; 7<sup>x<sup>2<\/sup><\/sup><span style=\"font-weight: 400;\">!<\/span><\/p>\n<p><b>Pembahasan:<\/b><\/p>\n<p><span style=\"font-weight: 400;\">Untuk menentukan solusinya, Quipperian harus menyamakan basis pada kedua ruas. Berdasarkan sifat-sifat eksponen diperoleh:<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-277885\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-20.png\" alt=\"\" width=\"139\" height=\"112\"><\/p>\n<p><span style=\"font-weight: 400;\">Oleh karena <\/span><i><span style=\"font-weight: 400;\">a<\/span><\/i><span style=\"font-weight: 400;\"> = 7 &gt; 1, maka berlaku:<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-277884\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-21.png\" alt=\"\" width=\"186\" height=\"111\"><\/p>\n<p><span style=\"font-weight: 400;\">Titik pembuat nol <\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\"> = 4 dan <\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\"> = 2.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Selanjutnya, Quipperian harus menempatkan titik pembuat nol dalam garis bilangan. Kemudian, tentukan tanda daerahnya dengan titik uji. Oleh karena tanda pertidaksamannya \u201c&lt;\u201d, maka bulatannya kosong dan titik pembuat nol tidak termasuk dalam nilai <\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-277883\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-22.png\" alt=\"\" width=\"349\" height=\"106\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-22.png 349w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2019\/12\/Eksponen-Matematika-Matematika-Kelas-10-22-300x91.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Jadi, himpunan penyelesaian dari pertidaksamaan eksponen di atas<\/span><sup>&nbsp;<\/sup><span style=\"font-weight: 400;\">adalah {<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">|<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i> <span style=\"font-weight: 400;\">\u2208<\/span> <i><span style=\"font-weight: 400;\">R<\/span><\/i><span style=\"font-weight: 400;\">, 2 &lt; <\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\"> &lt; 4}.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Nampaknya, cukup mudah ya materi persamaan dan pertidaksamaan eksponen ini? Quipperian tidak perlu khawatir, semua pembahasan lengkapnya bisa kamu dapatkan di Quipper Video. Quipper Video menyediakan ribuan latihan soal beserta pembahasannya yang bisa kamu gunakan kapanpun dan dimanapun. Tidak hanya itu, kamu juga akan dibimbing langsung oleh para tutor yang pastinya kece dan jago di bidangnya. So, tunggu apa lagi? Bersama Quipper Video, belajar jadi lebih mudah dan menyenangkan. Salam Quipper!<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><b>Penulis: Eka Viandari<\/b><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hai Quipperian, bagaimana kabarnya? Semoga selalu sehat dan tetap semangat, ya! Pernahkah kamu mendengar istilah sensus penduduk? Sensus penduduk adalah proses yang dilakukan pemerintah&hellip;<\/p>\n","protected":false},"author":99400369,"featured_media":277910,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_monsterinsights_skip_tracking":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_wpcom_ai_launchpad_first_post":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[679384888,679384865],"tags":[],"ppma_author":[679386827,679386836],"class_list":["post-277878","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mapel","category-matematika"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Eksponen Matematika - Matematika Kelas 10 - Quipper Blog<\/title>\n<meta name=\"description\" content=\"Belajar Matematika memang enggak ada habisnya, ya! 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