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PANGKAT, AKAR, DAN LOGARITMA

PANGKAT, AKAR, DAN LOGARITMA. WIDITA KURNIASARI, SE, ME. Pengertian Pangkat dari bilangan. Suatu indeks yang menunjukkan banyaknya perkalian bilangan yang sama secara beruntun Misalnya : 7 5 = 7 x 7 x 7 x 7 x 7 5 7 = 5 x 5 x 5 x 5 x 5 x 5 x 5

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PANGKAT, AKAR, DAN LOGARITMA

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  1. PANGKAT, AKAR, DAN LOGARITMA WIDITA KURNIASARI, SE, ME

  2. PengertianPangkatdaribilangan • Suatuindeks yang menunjukkanbanyaknyaperkalianbilangan yang samasecaraberuntun • Misalnya: 75 = 7 x 7 x 7 x 7 x 7 57 = 5 x 5 x 5 x 5 x 5 x 5 x 5 0,35 = 0,3 x 0,3 x 0,3 x 0,3 x 0,3 105 = 10 x 10 x 10 x 10 x 10 • Notasipemangkatanberfaedah pula untukmeringkasbilangan-bilangankelipatanperkaliansepuluh yang nilainyasangatbesaratausangatkecil • Misalnya: 10-5 = 1/100.000

  3. KaidahPemangkatanBilangan • x0 = 1 (x ≠ 0) • x1 = x • 0 n = 0 • x-a = 1/xa • xa/b = b√xa • (x/y)a = xa/ya • (x a)b = xab • x2³ = x8

  4. KaidahPerkalianBilanganBerpangkat • xa. xb = xa+b • xa.ya = (xy)a • xa: xb = xa-b • xa: ya=(x/y)a

  5. AKAR • a√m = x ; jikaxa = m (x adalah basis) • contoh: 2√9 = 3 3√64= 4 • b√x = x 1/b • b√xa = xa/b • b√xy = b√xb√y • b√x/y = b√x/b√y • mb√xa ± n b√xa= (m±n) b√xa

  6. LOGARITMA • Bentukpangkat : xa = m • Bentukakar : a√m = x • Bentuklogaritma : xlog m = a Contoh : • 6log 36 = 2 • 5log 625 = 4 • 7log 49 = 2 • 3log m = 10 ; m=? • 10log 10.000 = a ; a=?

  7. KAIDAH-KAIDAH LOGARITMA • xlog x = 1 • xlog 1 = 0 • xlogxa= a • xlog ma = a xlog m • xxlog m = m • xlog m n = xlog m + xlog n • xlog m/n = xlog m - xlog n • xlog m mlog x = 1 • xlog m . mlog n . nlog x = 1

  8. LatihanSoal 1. Sederhanakanbentuk-bentukberikutini: • 45. 47.4-6 • 54 . 34 . (-6)4 2. Sederhanakandankemudianselesaikan: • 10√5 + 2√5 – 7√5 • (3√27) (5.3√125) 3. Ubahlah kedalam bentuk logaritma: • 54 • 3√64 • Apabila x dan y masing-masing adalah 100 dan 50, hitunglah: • Log xy • Log x/y Silahkan baca Buku Dumairy, Matematika Terapan Untuk Bisnis dan Ekonomi hal.29-41

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