7.044. $\log _{x} 9 x^{2} \cdot \log _{3}^{2} x=4$.
## Solution.

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

## We have

$$
\frac{\log _{3} 9 x^{2}}{\log _{3} x} \cdot \log _{3}^{2} x=4, \quad\left(\log _{3} 9+\log _{3} x^{2}\right) \log _{3} x=4, \log _{3}^{2} x+\log _{3} x-2=0
$$

Solving this equation as a quadratic equation in terms of $\log _{3} x$, we find $\left(\log _{3} x\right)_{1}=-2$, from which $x_{1}=\frac{1}{9},\left(\log _{3} x\right)_{2}=1$, from which $x_{2}=3$.

Answer: $\frac{1}{9} ; 3$.