$\begin{align}  & {{\log }_{9}}a=2+{{\log }_{3}}b \\ & {{\log }_{9}}a-{{\log }_{3}}b=2 \\ & {{\log }_{{{3}^{2}}}}a-{{\log }_{3}}b=2 \\ & \tfrac{1}{2}{{\log }_{3}}a-{{\log }_{3}}b=2\left| {{\log }_{{{x}^{n}}}}y= \right.\tfrac{1}{n}{{\log }_{x}}y \\ & {{\log }_{3}}{{a}^{\tfrac{1}{2}}}-{{\log }_{3}}b=2 \\ & {{\log }_{3}}\left( \frac{{{a}^{\tfrac{1}{2}}}}{b} \right)=2 \\ & \frac{{{a}^{\tfrac{1}{2}}}}{b}={{3}^{2}} \\ & {{a}^{\tfrac{1}{2}}}{{b}^{-1}}=9 \\\end{align}$