# How do you find the inverse of y=(1/2)^x?

##### 1 Answer
Dec 26, 2015

$\textcolor{w h i t e}{\times} x = - {\log}_{2} y$

#### Explanation:

$\textcolor{w h i t e}{\times} y = {\left(\frac{1}{2}\right)}^{x}$

$\implies x = {\log}_{\frac{1}{2}} y$
$\implies x = {\log}_{{2}^{-} 1} y$
$\implies x = - {\log}_{2} y$