7.207. $\log _{\sqrt{a}} \frac{\sqrt{2 a-x}}{a}-\log _{1 / a} x=0$.

7.207. $\log _{\sqrt{a}} \frac{\sqrt{2 a-x}}{a}-\log _{1 / a} x=0$.
Solution.

Domain of definition: $\left\{\begin{array}{l}0<a \neq 1, \\ 2 a-x \geq 0\end{array} \Leftrightarrow\left\{\begin{array}{l}0<\dot{a} \neq 1, \\ x \leq 2 a .\end{array}\right.\right.$

From the condition we have

$$
\begin{aligned}
& \frac{\log _{a} \frac{\sqrt{2 a-x}}{a}}{\log _{a} \sqrt{a}}-\frac{\log _{a} x}{\log _{a} \frac{1}{a}}=0 \Leftrightarrow \log _{a}(2 a-x)+\log _{a} x=2 \Leftrightarrow \\
& \Leftrightarrow \log _{a} x(2 a-x)=2
\end{aligned}
$$

from which $x^{2}-2 a x+a^{2}=0,(x-a)^{2}=0 \Leftrightarrow x=a$.

Answer: $a$, where $0<a \neq 1$.