Answer
$x=-3$
Work Step by Step
We know that if $b\gt0$ and $b\ne1$, then $y=log_{b}x$ is equivalent to $x=b^{y}$ (where $x\gt0$ and $y$ is a real number).
Therefore, $log_{3}\frac{1}{27}=x$ is equivalent to $3^{x}=\frac{1}{27}$.
Therefore, $x=-3$, because $3^{-3}=\frac{1}{3^{3}}=\frac{1}{27}$.