$\begin{array}{l}
\,\,\,\,\,\,\,\,{9^x}{.81^x} = {3^{2010}}\\
\Rightarrow {\left( {{3^2}} \right)^x}.{\left( {{3^4}} \right)^x} = {3^{2010}}\\
\Rightarrow {3^{2x}}{.3^{4x}} = {3^{2010}}\\
\Rightarrow {3^{6x}} = {3^{2010}}\\
\Rightarrow 6x = 2010\\
\Rightarrow x = 2010:6\\
\Rightarrow x = 335
\end{array}$