BAB IA Perpangkatan/Eksponen

Perpangkatan/Eksponen:

Pengertian:

a^{n}~= a x a x a x …. x a (n faktor)

Sifat-sifat Perpangkatan :

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

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

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

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

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

Persamaan Pangkat:

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

    berlaku untuk a > 0 dan a \neq 1

Pertidaksamaan Pangkat:

Untuk a > 1

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

Untuk 0 < a < 1

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

This entry was posted on Wednesday, August 29th, 2012 at 3:43 am and is filed under Matematika SMA. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.



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