Answer
$log_{3}\frac{1}{81}=-4$
Work Step by Step
We are given $3^{-4}=\frac{1}{81}$.
If $b\gt0$ and $b\ne1$, then $y=log_{b}x$ means $x=b^{y}$ for every $x$ and every real number $y$.
Therefore, $3^{-4}=\frac{1}{3^{4}}=\frac{1}{81}$ is equivalent to $log_{3}\frac{1}{81}=-4$.
