Answer
2.
Work Step by Step
${{\log }_{9}}81$
$\begin{align}
& {{\log }_{9}}81={{\log }_{9}}{{9}^{2}} \\
& =2{{\log }_{9}}9
\end{align}$
Using log rules:
$\begin{align}
& {{\log }_{9}}81=2\left( 1 \right) \\
& =2
\end{align}$