Answer
$-2$
Work Step by Step
The definition of the logarithmic function says that $y=\log_a{x}$ if and only if $a^y=x$. Also, $a\gt0,a\ne1$ and $x\gt0$.
Hence $\log_3 {\frac{1}{9}}=y$, then $3^y=\frac{1}{9}$ and we know that $\frac{1}{9}=3^{-2}.$
Thus, $3^y=3^{-2}$. We know that $a^b=a^c\longrightarrow b=c$ if $a\ne1,a\ne-1$ (which applies here), hence $y=-2$.
