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_{3}\left(\frac{1}{81}\right)\ \ $ means $\ \ 3^{y}=\displaystyle \frac{1}{81} .$
Since
$\displaystyle \frac{1}{81}=81^{-1}=(3^{4})^{-1}=3^{-4},$
$y=-4$