7.174. $3^{\log _{3}^{2} x}+x^{\log _{3} x}=162$.

Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.

7.174. $3^{\log _{3}^{2} x}+x^{\log _{3} x}=162$.
## Solution.

Domain of definition: $0<x \neq 1$.

Rewrite the equation as

$$
\begin{aligned}
& \left(3^{\log _{3} x}\right)^{\log _{3} x}+x^{\log _{3} x}=162 \Leftrightarrow x^{\log _{3} x}+x^{\log _{3} x}=162 \Leftrightarrow \\
& \Leftrightarrow x^{\log _{3} x}=81 \Leftrightarrow \log _{3}^{2} x=4
\end{aligned}
$$

Then $\left(\log _{3} x\right)_{1}=-2$ or $\left(\log _{3} x\right)_{2}=2$, from which $x_{1}=\frac{1}{9}, x_{2}=9$.

Answer: $\frac{1}{9} ; 9$.