BAB IA Perpangkatan/Eksponen

By | August 29, 2012

Perpangkatan/Eksponen:

Pengertian:

$latex a^{n}~$= a x a x a x …. x a (n faktor)

Sifat-sifat Perpangkatan :

  1. $latex a^{m}.a^{n}= a^{m+n}$
  2. $latex a^{m}:a^{n} = \frac{a^{m}}{a^{n}}= a^{m-n}; a \neq 0$
  3. $latex (a^{m})^{n} = a^{mn} $
  4. $latex (a.b)^{n} = a^{n}.b^{n} $
  5. $latex \left ( \frac{a}{b} \right )^{n}= \frac{a^{n}}{b^{n}}~ ;b\neq 0 $
  6. $latex a^{0}= 1 ; a \neq 0$

    $latex a^{n-n}= \frac {a^{n}}{a^{n}}= 1$

  7. $latex a^{-n}= \frac {1}{a^{n}}; a \neq 0$

    $latex a^{0-n}=\frac {a^{0}}{a^{n}}= a^{-n}$

  8. $latex a^{\frac {m}{n}}= \sqrt[n]{a^{m}}$

Persamaan Pangkat:

  1. Jika $latex a^{f(x)} = a^{g(x)} \Leftrightarrow$ f(x) = g(x)
  2. Jika $latex a^{f(x)} = a^{p} \Leftrightarrow$ f(x) = p

    berlaku untuk a > 0 dan $latex a \neq 1$

Pertidaksamaan Pangkat:

Untuk a > 1

  1. Jika $latex a^{f(x)} > a^{g(x)} \Leftrightarrow$ f(x) > g(x)
  2. Jika $latex a^{f(x)} < a^{g(x)} \Leftrightarrow$ f(x) < g(x)

Untuk 0 < a < 1

  1. Jika $latex a^{f(x)} > a^{g(x)} \Leftrightarrow$ f(x) < g(x)
  2. Jika $latex a^{f(x)} < a^{g(x)} \Leftrightarrow$ f(x) > g(x)

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