Answer
$log_{2}\frac{1}{16}=-4$
Work Step by Step
If $b\gt0$ and $b\ne1$, then $y=log_{b}x$ means $x=b^{y}$ for every $x\gt0$ and every real number $y$.
Therefore, $2^{-4}=\frac{1}{16}$ is equivalent to $log_{2}\frac{1}{16}=-4$.
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