7.043. $\lg \left(81 \cdot \sqrt[3]{3^{x^{2}-8 x}}\right)=0$.

7.043. $\lg \left(81 \cdot \sqrt[3]{3^{x^{2}-8 x}}\right)=0$.
## Solution.

We have $81 \cdot \sqrt[3]{3^{x^{2}-8 x}}=1, 3^{\frac{x^{2}-8 x}{3}}=3^{-4}$, from which $\frac{x^{2}-8 x}{3}=-4, x^{2}-8 x+12=0$; $x_{1}=2 ; x_{2}=6$.

Answer: $2 ; 6$.