7.098. $\lg \sqrt{x-3}+\lg \sqrt{x+3}=2-0.5 \lg 625$.
Solution.

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

## We have

$\lg \sqrt{x-3}+\lg \sqrt{x+3}=\lg 100-\lg 25, \lg \sqrt{x^{2}-9}=\lg 4, \sqrt{x^{2}-9}=4$, from which $x^{2}=25, x_{1}=-5, x_{2}=5, x_{1}=-5$ does not satisfy the domain of definition.

Answer: 5 .