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How do you find the inverse of $y = {(\frac{1}{2})}^{x}$ $y=(1/2)^x$ ?

1 Answer

Dec 26, 2015

$\times x = - {log}_{2} y$ $color(white)xxx=-log_2 y$

Explanation:

$\times y = {(\frac{1}{2})}^{x}$ $color(white)xxy=(1/2)^x$

$\Rightarrow x = {log}_{\frac{1}{2}} y$ $=>x=log_(1/2) y$
$\Rightarrow x = {log}_{2^{- 1}}^{- 1} y$ $=>x=log_(2^-1) y$
$\Rightarrow x = - {log}_{2} y$ $=>x=-log_2 y$

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