7.111. $\frac{1}{3} \lg \left(271+3^{2 \sqrt{x}}\right)+\lg 10=2$.
## Solution.

Domain: $x \geq 0$.

From the condition $\frac{1}{3} \lg \left(271+3^{2 \sqrt{x}}\right)+1=2, \lg \left(271+3^{2 \sqrt{x}}\right)=3$. Then $271+3^{2 \sqrt{x}}=$ $=1000,3^{2 \sqrt{x}}=3^{6}$, from which $\sqrt{x}=3, x=9$.

Answer: 9.