7.035. $\log _{3}\left(81^{x}+3^{2 x}\right)=3 \log _{27} 90$.
## Solution.

From the condition $\log _{3}\left(81^{x}+3^{2 x}\right)=\log _{3} 90, 9^{2 x}+9^{x}-90=0$, from which we find $9^{x}=-10$, which is not suitable, or $9^{x}=9$, from which we have $x=1$.

Answer: 1.