{"id":58838,"date":"2022-06-13T18:00:29","date_gmt":"2022-06-13T11:00:29","guid":{"rendered":"https:\/\/superapp.id\/blog\/?p=58838"},"modified":"2022-06-13T15:53:48","modified_gmt":"2022-06-13T08:53:48","slug":"logaritma","status":"publish","type":"post","link":"https:\/\/superapp.id\/blog\/lifestyle\/logaritma\/","title":{"rendered":"Logaritma: Pengertian, Sifat, Fungsi, Rumus & Persamaannya"},"content":{"rendered":"

Salah satu materi dalam ilmu matematika yaitu logaritma. Materi ini merupakan kebalikan dari materi pemangkatan atau eksponensial. Secara sederhana, logaritma <\/span>digunakan untuk mencari besaran pangkat dari suatu bilangan yang telah diketahui hasil pangkatnya.<\/span><\/span><\/p>\n

Fungsi logaritma dalam kehidupan sehari-hari juga sangat penting. Selain digunakan dalam ilmu pengetahuan, ilmu ini juga dapat digunakan untuk <\/span>mengukur laju pertumbuhan penduduk hingga mengukur tingkat keterangan dari suatu bintang.<\/span><\/span><\/p>\n

Penjelasan lebih lanjut mengenai logaritma dapat disimak pada artikel berikut ini. Simak baik-baik, ya, Sedulur!<\/span><\/p>\n

BACA JUGA: <\/b>Rumus Luas Permukaan Kubus Beserta Contoh Soalnya<\/b><\/a><\/span><\/p>\n

Pengertian<\/b><\/span><\/h2>\n
\"logaritma\"<\/a>
<\/span> iStock<\/span><\/figcaption><\/figure>\n

Definisi logaritma dapat diketahui sebagai invers dari eksponen atau pemangkatan. Dengan kata lain, logaritma adalah suatu invers atau kebalikan dari pemangkatan yang digunakan dalam menentukan besaran pangkat pada sebuah bilangan pokok. Sederhananya, ilmu logaritma digunakan untuk mencari besaran pangkat dari suatu bilangan yang telah diketahui hasil pangkatnya.<\/span><\/p>\n

Ketika akan mencari nilai logaritma suatu bilangan, maka sama artinya dengan mencari pangkat dari suatu bilangan pokok. Oleh karena itu, hasilnya akan sesuai dengan yang telah diketahui. Untuk mencari logaritma suatu bilangan, dapat digunakan tabel logaritma biasa atau menggunakan beberapa sifat atau rumus identitas logaritma. Rumus tersebut dapat digunakan untuk menentukan nilai logaritma suatu bilangan dengan syarat atau kondisi tertentu<\/span>.<\/span><\/span><\/p>\n

Fungsi<\/b><\/span><\/h2>\n
\"logaritma\"<\/a>
<\/span> iStock<\/span><\/figcaption><\/figure>\n

Fungsi logaritma digunakan dalam ilmu matematika maupun ilmu pengetahuan alam (IPA). Logaritma juga digunakan pada ilmu kimia untuk menentukan orde reaksi maupun memilih koefisien serap bunyi yang pas. Tidak hanya itu, logaritma juga dipakai dalam mengukur laju pertumbuhan penduduk dan keuangan dalam menghitung bunga majemuk serta dalam bidang astronomi, logaritma dipakai sebagai alat perhitungan dalam mengukur tingkat keterangan dari suatu bintang.<\/span><\/p>\n

Logaritma banyak dimanfaatkan dalam sebuah kehidupan sehari-hari. Sebelum adanya kalkulator, logaritma dimanfaatkan untuk menghitung perhitungan eksponensial. Konsep logaritma juga dapat dipakai untuk melakukan perhitungan seismograf maupun alat pengukur kekuatan gempa, yang mana satuan skala richter memakai konsep logaritma di dalam perhitungannya.<\/span><\/p>\n

BACA JUGA: <\/b>Rumus Prisma Segitiga Beserta Sifat-Sifat & Contoh Soalnya<\/b><\/a><\/span><\/p>\n

Bentuk logaritma<\/b><\/span><\/h2>\n
\"logaritma\"<\/a>
<\/span> iStock<\/span><\/figcaption><\/figure>\n

Untuk lebih memahami materi ini, simak bentuk umum logaritma berikut.<\/span><\/p>\n

a<\/span>x <\/span>= b ↔ x <\/span>a<\/span>log b<\/span><\/span><\/p>\n

Dengan\u00a0 syarat b > 0, a > 0 dan a \u2260 1<\/span><\/p>\n

Keterangan:<\/span><\/p>\n

a= bilangan pokok atau basis logaritma<\/span><\/p>\n

b= numerus, yaitu bilangan yang akan dicari nilai logaritmanya<\/span><\/p>\n

x= hasil logaritma, dapat positif, nol atau bahkan negatif.<\/span><\/p>\n

Rumus<\/b><\/span><\/h2>\n
\"logaritma\"<\/a>
<\/span> iStock<\/span><\/figcaption><\/figure>\n

Berikut adalah rumus identitas dalam mencari nilai logaritma.<\/span><\/p>\n

a<\/span>log a<\/span>n<\/span> = n<\/span><\/span><\/p>\n

a<\/span>log a = 1<\/span><\/span><\/p>\n

a<\/span>log 1 = 0<\/span><\/span><\/p>\n

Pembuktian ketiga rumus di atas adalah sebagai berikut<\/span><\/p>\n

a<\/span>log a<\/span>n<\/span> = n \u2192 a<\/span>n<\/span> = a<\/span>n<\/span><\/span><\/p>\n

a<\/span>log a = 1 \u2192 a<\/span>1<\/span> = a<\/span><\/span><\/p>\n

a<\/span>log 1 = 0 \u2192 a<\/span>0<\/span> = 1<\/span><\/span><\/p>\n

BACA JUGA: <\/b>Balok: Pengertian, Sifat, Ciri-Ciri, Rumus dan Contoh Soalnya<\/b><\/a><\/span><\/p>\n

Persamaan<\/b><\/span><\/h2>\n
\"logaritma\"<\/a>
<\/span> iStock<\/span><\/figcaption><\/figure>\n

Persamaan logaritma adalah persamaan yang peubahnya terdapat dalam bilangan pokok atau numerusnya.<\/span><\/p>\n

Macam-macam bentuk persamaan logaritma :<\/span><\/p>\n

    \n
  1. a<\/span>log <\/span>\u00a0f(x) = <\/span>a<\/span>log <\/span>\u00a0p<\/span><\/span><\/li>\n
  2. f(x)<\/span>log<\/span> a = <\/span>g(x)<\/span>log a<\/span><\/span><\/li>\n
  3. a<\/span>log <\/span>\u00a0f(x) = <\/span>a<\/span>log <\/span>\u00a0g(x)\u00a0<\/span><\/span><\/li>\n
  4. f(x)<\/span>log <\/span>\u00a0g(x) = <\/span>f(x)<\/span>log <\/span>h(x)<\/span><\/span><\/li>\n
  5. a<\/span>log <\/span>\u00a0f(x) = <\/span>b<\/span>log <\/span>\u00a0f(x)\u00a0\u00a0<\/span><\/span><\/li>\n
  6. A<\/span><\/i>(<\/span>a<\/span>log<\/span> x<\/span><\/i>)<\/span>2<\/span> + <\/span>B<\/span><\/i>(<\/span>a<\/span>log<\/span> x<\/span><\/i>) + <\/span>C <\/span><\/i>= 0<\/span><\/span><\/li>\n
  7. f(x)<\/span>log <\/span>\u00a0g(x) = p\u00a0<\/span><\/span><\/li>\n<\/ol>\n

    Contoh : log (3x \u2013 1) = log (x \u2013 15) dan <\/span>x-1<\/span>log <\/span>\u00a016 = 2.<\/span><\/span><\/p>\n

    Sifat logaritma<\/b><\/span><\/h2>\n
    \"logaritma\"<\/a>
    <\/span> iStock<\/span><\/figcaption><\/figure>\n

    Berikut adalah beberapa sifat logaritma tersebut.<\/span><\/p>\n

    Sifat 1 (Perkalian logaritma)<\/h3>\n

    a<\/span>log (b \u00d7 c) = <\/span>a<\/span>log b + <\/span>a <\/span>log c<\/span><\/span><\/p>\n

    Sifat 2 (Pembagian logaritma)<\/h3>\n

    a<\/span>log (b\/c) = <\/span>a<\/span>log b \u2212 <\/span>a <\/span>log c<\/span><\/span><\/p>\n

    Sifat 3 (Perpangkatan logaritma)<\/h3>\n

    a<\/span>log b<\/span>n<\/span> = n x <\/span>a<\/span>log b<\/span><\/span><\/p>\n

    Sifat 4 (Pengubahan bilangan pokok logaritma 1)<\/h3>\n

    a<\/span>log b = <\/span>n <\/span>log b\/<\/span>n <\/span>log a<\/span><\/span><\/p>\n

    Sifat 5 (Pengubahan bilangan pokok logaritma 2)<\/h3>\n

    a<\/span>log b = 1\/<\/span> b<\/span>log a<\/span><\/span><\/p>\n

    Sifat 6 (Perluasan sifat perkalian logaritma)<\/h3>\n

    a<\/span>log b \u00d7 <\/span>b<\/span>log c = <\/span>a<\/span>log c<\/span><\/span><\/p>\n

    Sifat 7 (Perluasan sifat perpangkatan logaritma 1)<\/h3>\n

    a<\/span>n<\/span>log b<\/span>m<\/span> = <\/span>m\/n \u00d7 <\/span>a<\/span>log b<\/span><\/span><\/p>\n

    Sifat 8 (Perluasan sifat perpangkatan logaritma 2)<\/h3>\n

    a<\/span>n<\/span>log b<\/span>m<\/span> = <\/span>a<\/span>log b\u00a0<\/span><\/span><\/p>\n

    Sifat 9 (Perluasan dari bentuk umum logaritma)<\/h3>\n

    a<\/span>alog b<\/span> = b<\/span><\/span><\/p>\n

    Sifat 10 (Invers pembagian logaritma)<\/h3>\n

    a<\/span>log (b\/c) = \u2212 <\/span>a<\/span>log (c\/b)<\/span><\/span><\/p>\n

    BACA JUGA: <\/b>Jajar Genjang: Pengertian, Sifat, Rumus & Contoh Soalnya<\/b><\/a><\/span><\/p>\n

    Pembuktian logaritma<\/b><\/span><\/h2>\n
    \"logaritma\"<\/a>
    <\/span> iStock<\/span><\/figcaption><\/figure>\n

    Berikut adalah pembuktian dari sifat-sifat logaritma di atas.<\/span><\/p>\n

    Pembuktian sifat 1<\/b>\u00a0<\/span><\/span><\/h3>\n

    Misalkan<\/span><\/p>\n

    a<\/span>log b = n maka a<\/span>n<\/span> = b<\/span><\/span><\/p>\n

    a<\/span>log c = m maka a<\/span>m<\/span> = c<\/span><\/span><\/p>\n

    b \u00d7 c = a<\/span>n <\/span>\u00d7 a<\/span>m<\/span><\/span><\/p>\n

    dengan menggunakan sifat operasi hitung bilangan berpangkat diperoleh<\/span><\/p>\n

    b \u00d7 c = a<\/span>n + m<\/span> sehingga<\/span><\/span><\/p>\n

    a<\/span>log (b \u00d7 c) = n + m, karena n = <\/span>a<\/span>log b dan m = <\/span>a<\/span>log c maka<\/span><\/span><\/p>\n

    a<\/span>log (b \u00d7 c) = <\/span>a<\/span>log b + <\/span>a <\/span>log c<\/span><\/span><\/p>\n

    Pembuktian sifat 2\u00a0<\/b><\/span><\/h3>\n

    Misalkan<\/span><\/p>\n

    a<\/span>log b = n maka a<\/span>n<\/span> = b<\/span><\/span><\/p>\n

    a<\/span>log c = m maka a<\/span>m<\/span> = c<\/span><\/span><\/p>\n

    b\/c = a<\/span>n <\/span>\/a<\/span>m<\/span><\/span><\/p>\n

    dengan menggunakan sifat operasi hitung bilangan berpangkat diperoleh<\/span><\/p>\n

    b\/c = a<\/span>n \u2212 m<\/span> sehingga<\/span><\/span><\/p>\n

    a<\/span>log (b\/c) = n \u2212 m, karena n = <\/span>a<\/span>log b dan m = <\/span>a<\/span>log c maka<\/span><\/span><\/p>\n

    a<\/span>log (b\/c) = <\/span>a<\/span>log b \u2212 <\/span>a <\/span>log c<\/span><\/span><\/p>\n

    Pembuktian sifat 3\u00a0<\/b><\/span><\/h3>\n

    Dari sifat 1 logaritma,<\/span><\/p>\n

    a <\/span>log b + <\/span>a <\/span>log b = <\/span>a<\/span>log (b \u00d7 b)<\/span><\/span><\/p>\n

    2 <\/span>a<\/span>log b = <\/span>a<\/span>log b<\/span>2<\/span><\/span><\/p>\n

    Dengan cara yang sama:<\/span><\/p>\n

    a<\/span>log b<\/span>2<\/span> + <\/span>a <\/span>log b = <\/span>a<\/span>log (b<\/span>2<\/span> \u00d7 b)<\/span><\/span><\/p>\n

    2 <\/span>a<\/span>log b + <\/span>a<\/span>log b = <\/span>a<\/span>log b<\/span>3<\/span><\/span><\/p>\n

    3 <\/span>a<\/span>log b = <\/span>a<\/span>log b<\/span>3<\/span><\/span><\/p>\n

    Dengan cara yang sama:<\/span><\/p>\n

    a<\/span>log b<\/span>3<\/span> + <\/span>a<\/span>log b = <\/span>a<\/span>log (b<\/span>3<\/span> \u00d7 b)<\/span><\/span><\/p>\n

    3 <\/span>a<\/span>log b + <\/span>a<\/span>log b = <\/span>a<\/span>log b<\/span>4<\/span><\/span><\/p>\n

    4 <\/span>a<\/span>log b = <\/span>a<\/span>log b<\/span>4<\/span><\/span><\/p>\n

    Dengan demikian dapat disimpulkan:<\/span><\/p>\n

    n <\/span>a <\/span>log b = <\/span>a<\/span>log b<\/span>n<\/span><\/span><\/p>\n

    atau<\/span><\/p>\n

    a<\/span>log b<\/span>n<\/span> = n \u00d7 <\/span>a<\/span>log b<\/span><\/span><\/p>\n

    Pembuktian sifat 4<\/b><\/span><\/h3>\n

    a<\/span>log b = m maka b = a<\/span>m<\/span><\/span><\/p>\n

    n<\/span>log b = <\/span>n<\/span>log a<\/span>m<\/span><\/span><\/p>\n

    n<\/span>log b = m \u00d7 <\/span>n<\/span>log a<\/span><\/span><\/p>\n

    m = <\/span>n<\/span>log b\/<\/span> n<\/span>log a<\/span><\/span><\/p>\n

    a<\/span>log b = <\/span>n <\/span>log b\/<\/span> n <\/span>log a<\/span><\/span><\/p>\n

    Pembuktian sifat 5\u00a0<\/b><\/span><\/h3>\n

    Sifat logaritma yang ke-5 ini adalah sifat logaritma ke-4 dengan n = b.<\/span><\/p>\n

    a<\/span>log b = <\/span>n <\/span>log b\/ <\/span>n <\/span>log a<\/span><\/span><\/p>\n

    a<\/span>log b = <\/span>b<\/span>log b\/<\/span> b<\/span>log a<\/span><\/span><\/p>\n

    a<\/span>log b = 1\/<\/span> b<\/span>log a<\/span><\/span><\/p>\n

    Pembuktian sifat 6\u00a0<\/b><\/span><\/h3>\n

    Dengan menggunakan sifat logaritma nomor 4 di atas maka:<\/span><\/p>\n

    a<\/span>log b = <\/span>n <\/span>log b\/<\/span>n <\/span>log a<\/span><\/span><\/p>\n

    b<\/span>log c = <\/span>n<\/span>log c\/<\/span>n<\/span>log b<\/span><\/span><\/p>\n

    sehingga<\/span><\/p>\n

    a<\/span>log b \u00d7 <\/span>b<\/span>log c = (<\/span>n<\/span>log b\/<\/span>n<\/span>log a) \u00d7 (<\/span>n<\/span>log c\/<\/span>n<\/span>log b)<\/span><\/span><\/p>\n

    a<\/span>log b \u00d7 <\/span>b<\/span>log c = <\/span>n<\/span>log c\/<\/span> n<\/span>log a<\/span><\/span><\/p>\n

    a<\/span>log b \u00d7 <\/span>b<\/span>log c = <\/span>a<\/span>log c<\/span><\/span><\/p>\n

    Pembuktian sifat 7<\/b><\/span><\/h3>\n

    Misalkan<\/span><\/p>\n

    a<\/span>n<\/span>log b<\/span>m<\/span> = c maka (a<\/span>n<\/span>)<\/span>c<\/span> = bm<\/span><\/span><\/p>\n

    (a<\/span>n<\/span>)<\/span>c<\/span> = b<\/span>m<\/span><\/span><\/p>\n

    a<\/span>n\u00d7c<\/span> = b<\/span>m<\/span><\/span><\/p>\n

    b = <\/span>m<\/span>\u221a(a<\/span>nc<\/span>)<\/span><\/span><\/p>\n

    b = a <\/span>nc\/m<\/span> (bentuk pangkat ini kita ubah menjadi bentuk logaritma)<\/span><\/span><\/p>\n

    a<\/span>log b = nc\/m (ruas kanan dan kiri dikalikan m\/n)<\/span><\/span><\/p>\n

    m\/n \u00d7 <\/span>a<\/span>log b = c<\/span><\/span><\/p>\n

    a<\/span>n<\/span>log b<\/span>m<\/span> = <\/span>m\/n \u00d7 <\/span>a<\/span>log <\/span>b<\/span><\/span><\/p>\n

    Pembuktian sifat 8\u00a0<\/b><\/span><\/h3>\n

    Sama dengan pembuktian sifat 7 logaritma.<\/span><\/p>\n

    Pembuktian sifat 9\u00a0<\/b><\/span><\/h3>\n

    Misalkan <\/span>a<\/span>log b = c maka a<\/span>c<\/span> = b, sehingga<\/span><\/span><\/p>\n

    a<\/span>alog b<\/span> = a<\/span>c<\/span> = b<\/span><\/span><\/p>\n

    a<\/span>alog b<\/span> = b<\/span><\/span><\/p>\n

    Pembuktian sifat 10<\/b><\/span><\/h3>\n

    Sifat 10 logaritma dapat dibuktikan dengan menggunakan sifat 2 logaritma, pembuktiannya adalah sebagai berikut:<\/span><\/p>\n

    a<\/span>log (b\/c) = <\/span>a<\/span>log b \u2212 <\/span>a<\/span>log c<\/span><\/span><\/p>\n

    a<\/span>log (b\/c) = \u2212 (<\/span>a<\/span>log c \u2212 <\/span>a<\/span>log b)<\/span><\/span><\/p>\n

    a<\/span>log (b\/c) = \u2212 {<\/span>a<\/span>log (c\/b)}<\/span><\/span><\/p>\n

    a<\/span>log (b\/c) = \u2212 <\/span>a<\/span>log (c\/b)<\/span><\/span><\/p>\n

    BACA JUGA: <\/b>Rumus Keliling Lingkaran Beserta Contoh Soal & Pembahasan<\/b><\/a><\/span><\/p>\n

    Contoh soal\u00a0\u00a0<\/b><\/span><\/h2>\n
    \"logaritma\"<\/a>
    <\/span> iStock<\/span><\/figcaption><\/figure>\n

    Berikut adalah contoh soal logaritma sesuai dengan sifat-sifatnya.<\/span><\/p>\n

    Sederhanakanlah:<\/span><\/strong><\/p>\n

      \n
    1. 2<\/span>log 4 + <\/span>2<\/span>log 8<\/span><\/span><\/li>\n
    2. 5<\/span>log \u00bd + <\/span>5<\/span>log 50<\/span><\/span><\/li>\n<\/ol>\n

      Jawab:<\/b><\/span><\/p>\n

        \n
      1. 2<\/span>log 4 + <\/span>2<\/span>log 8 = <\/span>2<\/span>log (4 \u00d7 8) = <\/span>2<\/span>log 32 = 5<\/span><\/span><\/li>\n
      2. 5<\/span>log \u00bd + <\/span>5<\/span>log 50 = <\/span>5<\/span>log (\u00bd \u00d7 50) = <\/span>5<\/span>log 25 = 2<\/span><\/span><\/li>\n<\/ol>\n

        Sederhanakanlah:<\/span><\/strong><\/p>\n

          \n
        1. 7<\/span>log 217 \u2212 <\/span>7<\/span>log 31<\/span><\/span><\/li>\n
        2. log 0,05 \u2212 log 5<\/span><\/li>\n<\/ol>\n

          Jawab:<\/b><\/span><\/p>\n

            \n
          1. 7<\/span>log 217 \u2212 <\/span>7<\/span>log 31 = <\/span>7<\/span>log (217\/31) = <\/span>7<\/span>log 7 = 1<\/span><\/span><\/li>\n
          2. log 0,05 \u2212 log 5 = log (0,05\/5) = log 0,01 = \u22122<\/span><\/li>\n<\/ol>\n

            Sederhanakanlah:<\/span><\/strong><\/p>\n

              \n
            1. 2 log 25 \u2013 3 log 5 + log 20<\/span><\/li>\n
            2. \u00bd <\/span>2<\/span>log 82 \u2013 3 <\/span>2<\/span>log 3 + <\/span>2<\/span>log 48<\/span><\/span><\/li>\n<\/ol>\n

              Jawab:<\/b><\/span><\/p>\n

                \n
              1. 2 log 25 \u2013 3 log 5 + log 20<\/span><\/li>\n<\/ol>\n

                = log 25<\/span>2<\/span> \u2013 log 5<\/span>3<\/span> + log 20<\/span><\/span><\/p>\n

                = log (25<\/span>2<\/span>\/5<\/span>3<\/span>) + log 20<\/span><\/span><\/p>\n

                = log 5 + log 20<\/span><\/p>\n

                = log (5 \u00d7 20)<\/span><\/p>\n

                = log 100\u00a0<\/span><\/p>\n

                = 2<\/span><\/p>\n

                  \n
                1. \u00bd <\/span>2<\/span>log 82 \u2013 3 <\/span>2<\/span>log 3 + <\/span>2<\/span>log 48<\/span><\/span><\/li>\n<\/ol>\n

                  = <\/span>2<\/span>log 82<\/span>\u00bd<\/span> \u2013 <\/span>2<\/span>log 3<\/span>3<\/span> + <\/span>2<\/span>log 48<\/span><\/span><\/p>\n

                  = <\/span>2<\/span>log (9\/27) + <\/span>2<\/span>log 48<\/span><\/span><\/p>\n

                  = <\/span>2<\/span>log 1\/3 + <\/span>2<\/span>log 48<\/span><\/span><\/p>\n

                  = <\/span>2<\/span>log (1\/3 \u00d7 48)<\/span><\/span><\/p>\n

                  = <\/span>2<\/span>log 16 = 4<\/span><\/span><\/p>\n

                  Soal:<\/span><\/strong><\/p>\n

                  Jika <\/span>2<\/span>log 3 = a, nyatakan bentuk logaritma <\/span>8 <\/span>log 3 ke dalam a.<\/span><\/span><\/p>\n

                  Jawab:<\/b><\/span><\/p>\n

                  8<\/span>log 3 = log 3\/log 8<\/span><\/span><\/p>\n

                  8<\/span>log 3 = log 3\/log 2<\/span>3<\/span><\/span><\/p>\n

                  8<\/span>log 3 = 1\/3 \u00d7 (log 3\/log 2)<\/span><\/span><\/p>\n

                  8<\/span>log 3 = 1\/3 \u00d7 <\/span>2<\/span>log 3<\/span><\/span><\/p>\n

                  8<\/span>log 3 = 1\/3 a<\/span><\/span><\/p>\n

                  Soal:<\/span><\/strong><\/p>\n

                  Tentukan nilai dari <\/span>2<\/span>log 8 dan <\/span>64 <\/span>log 4!<\/span><\/span><\/p>\n

                  Jawab:<\/b><\/span><\/p>\n

                    \n
                  1. 2<\/span>log 8 = 1\/<\/span>8<\/span>log 2<\/span><\/span><\/li>\n<\/ol>\n

                    2<\/span>log 8 = 1\/<\/span>8<\/span>log 8<\/span>1\/3<\/span><\/span><\/p>\n

                    2<\/span>log 8 = 1\/(1\/3)<\/span><\/span><\/p>\n

                    2<\/span>log 8 = 3<\/span><\/span><\/p>\n

                      \n
                    1. 64<\/span>log 4 = 1\/<\/span>4<\/span>log 64<\/span><\/span><\/li>\n<\/ol>\n

                      64<\/span>log 4 = 1\/<\/span>4<\/span>log 4<\/span>3<\/span><\/span><\/p>\n

                      64<\/span>log 4 = 1\/3<\/span><\/span><\/p>\n

                      Soal:<\/span><\/strong><\/p>\n

                      Hitunglah nilai logaritma dari<\/span><\/span><\/p>\n

                        \n
                      1. 2<\/span>log 5 \u00d7 <\/span>5<\/span>log 64<\/span><\/span><\/li>\n
                      2. 2<\/span>log 25 \u00d7 <\/span>5<\/span>log 3 \u00d7 <\/span>3<\/span>log 32<\/span><\/span><\/li>\n<\/ol>\n

                        Jawab:<\/b><\/span><\/p>\n

                          \n
                        1. 2<\/span>log 5 \u00d7 <\/span>5<\/span>log 64 = <\/span>2<\/span>log 64 = <\/span>2<\/span>log 2<\/span>6<\/span> = 6<\/span><\/span><\/li>\n
                        2. 2<\/span>log 25 \u00d7 <\/span>5<\/span>log 3 \u00d7 <\/span>9<\/span>log 32<\/span><\/span><\/li>\n<\/ol>\n

                          = <\/span>2<\/span>log 5<\/span>2<\/span> \u00d7 <\/span>5<\/span>log 3 \u00d7 <\/span>3<\/span>log 2<\/span>5<\/span><\/span><\/p>\n

                          = 2 <\/span>2<\/span>log 5 \u00d7 <\/span>5<\/span>log 3 \u00d7 5 <\/span>3<\/span>log 2<\/span><\/span><\/p>\n

                          = 2 \u00d7 5 \u00d7 <\/span>2<\/span>log 5 \u00d7 <\/span>5<\/span>log 3 \u00d7 <\/span>3<\/span>log 2<\/span><\/span><\/p>\n

                          = 10 \u00d7 <\/span>2<\/span>log 2<\/span><\/span><\/p>\n

                          = 10 \u00d7 1<\/span><\/p>\n

                          = 10<\/span><\/p>\n

                          Soal:<\/strong><\/p>\n

                          Hitunglah nilai logaritma dari<\/p>\n

                            \n
                          1. a) <\/span>22<\/span>log 4<\/span>3<\/span><\/span><\/li>\n
                          2. b) <\/span>24<\/span>log \u221a32<\/span><\/span><\/li>\n<\/ol>\n

                            Jawab:<\/b><\/span><\/p>\n

                              \n
                            1. a) <\/span>22<\/span>log 4<\/span>3<\/span> = 3\/2 \u00d7 log 4 = 3\/2(2) = 3<\/span><\/span><\/li>\n
                            2. b) <\/span>24<\/span>log \u221a32 = <\/span>24<\/span>log 32<\/span>\u00bd<\/span> = 1\/8 \u00d7 <\/span>2<\/span>log 32 = 1\/8 (5) = 5\/8<\/span><\/span><\/li>\n<\/ol>\n

                              Soal:<\/span><\/strong><\/p>\n

                              Jika <\/span>2<\/span>log 3 = a, nyatakan logaritma <\/span>8<\/span>log 27 ke dalam bentuk a<\/span><\/span><\/p>\n

                              Jawab:<\/b><\/span><\/p>\n

                              8<\/span>log 27 = <\/span>23<\/span>log 3<\/span>3<\/span> = <\/span>2<\/span>log 3 = a<\/span><\/span><\/p>\n

                              Sederhanakanlah:<\/strong><\/p>\n

                                \n
                              1. a) 2<\/span>2log 5<\/span><\/span><\/li>\n
                              2. b) 3<\/span>3log 4<\/span><\/span><\/li>\n
                              3. c) 5<\/span>5log 10<\/span><\/span><\/li>\n
                              4. d) 7<\/span>7log 25<\/span><\/span><\/li>\n<\/ol>\n

                                Jawab:<\/b><\/span><\/p>\n

                                  \n
                                1. a) 2<\/span>2log 5<\/span> = 5<\/span><\/span><\/li>\n
                                2. b) 3<\/span>3log 4<\/span> = 4<\/span><\/span><\/li>\n
                                3. c) 5<\/span>5log 10<\/span> = 10<\/span><\/span><\/li>\n
                                4. d) 7<\/span>7log 25<\/span> = 25<\/span><\/span><\/li>\n<\/ol>\n

                                  Soal:<\/span><\/strong><\/p>\n

                                  Tentukan nilai logaritma dari<\/span><\/p>\n

                                    \n
                                  1. 2<\/span>log (4\/2)<\/span><\/span><\/li>\n
                                  2. 4<\/span>log (32\/2)<\/span>\u00a0<\/span><\/span><\/li>\n<\/ol>\n

                                    Jawab:<\/b><\/span><\/p>\n

                                      \n
                                    1. 2<\/span>log (4\/2) = \u2212<\/span>2<\/span>log (2\/4) <\/span>\u00a0<\/span>= \u2212 <\/span>2<\/span>log \u00bd\u00a0 = \u2212 <\/span>2<\/span>log 2<\/span>\u22121<\/span> = \u2212 (\u22121) <\/span>2<\/span>log 2 = 1<\/span><\/span><\/li>\n
                                    2. 4<\/span>log (32\/2)<\/span> = \u2212<\/span>4<\/span>log (2\/32) = \u2212 <\/span>4<\/span>log (1\/16) = \u2212<\/span>4<\/span>log 4<\/span>-2<\/span> = \u2212 (\u22122) <\/span>4<\/span>log 4 = 2<\/span><\/span><\/li>\n<\/ol>\n

                                      <\/h4>

                                      No related posts found...<\/p><\/div><\/span><\/p>\n

                                      Nah, itulah informasi mengenai logaritma, beserta fungsi, rumus, dan persamaannya. Semoga dengan adanya contoh soal dan pembahasannya juga dapat membantu Sedulur dalam mempelajari ilmu matematika lebih baik lagi. Selamat belajar!<\/span><\/p>\n

                                      Mau belanja bulanan nggak pakai ribet? <\/span><\/i>Aplikasi Super<\/i><\/b> solusinya! Mulai dari sembako hingga kebutuhan rumah tangga tersedia lengkap. Selain harganya murah, Sedulur juga bisa merasakan kemudahan belanja lewat handphone. Nggak perlu keluar rumah, belanjaan pun langsung diantar.<\/span><\/i><\/span><\/p>\n

                                      Bagi Sedulur yang punya toko kelontong atau warung, bisa juga lho belanja grosir atau kulakan lewat <\/span><\/i>Aplikasi Super<\/i><\/b>. Harga dijamin lebih murah dan bikin untung makin melimpah.<\/span><\/i><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":24,"featured_media":59067,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[7992,3706,7993],"class_list":["post-58838","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-lifestyle","tag-logaritma","tag-matematika","tag-persamaan-logaritma"],"yoast_head":"\nLogaritma: Pengertian, Sifat, Fungsi, Rumus & Persamaannya<\/title>\n<meta name=\"description\" content=\"Salah satu materi dalam ilmu matematika yaitu logaritma. 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