Answer
-2.
Work Step by Step
${{\log }_{3}}\frac{1}{9}$
Apply the negative exponent rule:
$\begin{align}
& {{\log }_{3}}\frac{1}{9}={{\log }_{3}}{{9}^{-1}} \\
& ={{\log }_{3}}{{3}^{-2}} \\
& =-2{{\log }_{3}}3
\end{align}$
This gives:
$\begin{align}
& {{\log }_{3}}\frac{1}{9}=-2\left( 1 \right) \\
& =-2
\end{align}$
