7.255. $25^{\log _{4} x}-5^{\log _{16} x^{2}+1}=\log _{\sqrt{3}} 9 \sqrt{3}-25^{\log _{16} x}$.
## Solution.

Domain of definition: $x>0$.

Rewrite the equation as

$5^{\log _{2} x}-5 \cdot 5^{\frac{1}{2} \log _{2} x}=5-5^{\frac{1}{2} \log _{2} x} \Leftrightarrow 5^{\log _{2} x}-4 \cdot 5^{\frac{1}{2} \log _{2} x}-5=0$.

Solving this equation as a quadratic equation in terms of $5^{\frac{1}{\log _{2} x}}$, we get
$5^{\frac{1}{2} \log _{2} x}=-1$ (no solutions), or $5^{\frac{1}{2} \log _{2} x}=5 \Rightarrow \frac{1}{2} \log _{2} x=1, \log _{2} x=2$, $x=2^{2}=4$.

Answer: 4.