$7.65 \quad 3^{\log _{3}^{2} x}+x^{\log _{3} x}=162$.
7.65 We have $3^{\log _{3}^{2} x}=\left(3^{\log _{3} x}\right)^{\log _{3} x}=x^{\log _{3} x}$. Then the equation will be

$2 x^{\log _{3} x}=162$, or $x^{\log _{3} x}=81$.

Since $x>0$, we can take the logarithm of both sides with base 3:

$$
\log _{3}^{2} x=4 \Rightarrow \log _{3} x= \pm 2 \Rightarrow x_{1}=\frac{1}{9}, x_{2}=9
$$

Answer: $x_{1}=\frac{1}{9}, x_{2}=9$