7.039. $\lg \left(10^{\lg \left(x^{2}-21\right)}\right)-2=\lg x-\lg 25$.
## Solution.

Domain of definition: $\left\{\begin{array}{l}x^{2}-21>0, \\ x>0,\end{array} x>\sqrt{21}\right.$.

From the condition we have

$$
\lg \left(x^{2}-21\right)-\lg 100=\lg x-\lg 25, \lg \frac{x^{2}-21}{100}=\lg \frac{x}{25}, \quad \frac{x^{2}-21}{100}=\frac{x}{25}
$$

We obtain the quadratic equation $x^{2}-4 x-21=0$, the roots of which are $x_{1}=7, x_{2}=-3 ; x_{2}=-3$ does not satisfy the domain of definition.

Answer: 7.