7.046. $\lg (5-x)+2 \lg \sqrt{3-x}=1$.

7.046. $\lg (5-x)+2 \lg \sqrt{3-x}=1$.
## Solution.

Domain of definition: $\quad\left\{\begin{array}{l}5-x>0, \\ 3-x>0,\end{array}, x<3\right.$.

We have $\lg (5-x)+\lg (3-x)=1, \lg (5-x)(3-x)=1$, hence $(5-x)(3-x)=10$, $x^{2}-8 x+5=0$. Then $x_{1}=4-\sqrt{11}, x_{2}=4+\sqrt{11} ; x_{2}=4+\sqrt{11}$ does not satisfy the domain of definition.

Answer: $4-\sqrt{11}$.