7.252. $\frac{2}{15}\left(16^{\log _{9} x+1}-16^{\log _{3} \sqrt{x}}\right)+16^{\log _{3} x}-\log _{\sqrt{5}} 5 \sqrt{5}=0$.
## Solution.

Domain of definition: $x>0$.

Rewrite the equation as

$$
\begin{aligned}
& \frac{2}{15}\left(16 \cdot 16^{\frac{1}{2} \log _{3} x}-16^{\frac{1}{2} \log _{3} x}\right)+16^{\log _{3} x}-3=0 \Leftrightarrow \\
& \Leftrightarrow 16^{\log _{3} x}+2 \cdot 16^{\frac{\log _{3} x}{2}}-3=0
\end{aligned}
$$

Solving this equation as a quadratic in terms of $16^{\frac{\log _{3} x}{2}}$, we get $16^{\frac{\log _{3} x}{2}}=-3$ (no solutions), or $16^{\frac{\log _{3} x}{2}}=16^{0}$, from which $\frac{\log _{3} x_{2}}{2}=0$, $x=1$.

Answer: 1.