Answer
$-4$
Work Step by Step
From the definition of logarithms,
for $a>0$, $a\neq 1$, and $x > 0$,
$y=\log_{a}x$ means $a^{y}=x$.
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$y=\displaystyle \log_{2}(\frac{1}{16})\ \ $ means $\ \ 2^{y}=\displaystyle \frac{1}{16} .$
Since
$\displaystyle \frac{1}{16}=16^{-1}=(2^{4})^{-1}=2^{-4},$
$y=-4$