How do you find the inverse of ${log 2}^{- x}$ $log 2^-x$ ?

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How do you find the inverse of ${log 2}^{- x}$ $log 2^-x$ ?

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Answer 1 · 2015-12-24T12:57:44

Step by Step process is given below.

Explanation:

$y = log (2^{- x})$ $y=log(2^(-x))$

Note (x,y) inverse is (y,x) to get the inverse function we need to do the following steps.

$1 .$ $1.$ swap $x$ $x$ and $y$ $y$
$x = log (2^{- y})$ $x=log(2^(-y))$

$2 .$ $2.$ solve for $y$ $y$

$x = - y \cdot log (2)$ $x=-y*log(2)$ using $log (a^{n}) = n log (a)$ $log(a^n) = nlog(a)$
$- x = log (2) y$ $-x=log(2)y$
$- \frac{x}{log (2)} = y$ $-x/log(2) =y$

The inverse function is $f^{- 1} (x) = - \frac{x}{log (2)}$ $f^-1(x) = -x/log(2)$

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How do you find the inverse of ${log 2}^{- x}$ $log 2^-x$ ?

1 Answer

Explanation:

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