9.124. $y=\log _{3}\left(0.64^{2-\log _{\sqrt{2}} x}-1.25^{8-\left(\log _{2} x\right)^{2}}\right)$.
## Solution.

Consider the inequality $0.64^{2-\log _{\sqrt{2}} x}-1.25^{8-\left(\log _{2} x\right)^{2}}>0 \Leftrightarrow$

$$
\Leftrightarrow 0.64^{2-\log _{\sqrt{2}} x}>1.25^{8-\left(\log _{2} x\right)^{2}} \Leftrightarrow\left(\frac{4}{5}\right)^{4-2 \log _{\sqrt{2}} x}>\left(\frac{4}{5}\right)^{\left(\log _{2} x\right)^{2}-8} \Leftrightarrow
$$

$\Leftrightarrow 4-2 \log _{\sqrt{2}} x>\log _{2}^{2} x-8$. Transitioning to base 2, we get $\log _{2}^{2} x+4 \log _{2} x-12>0$. Solving this inequality as a quadratic equation in terms of $\log _{2} x$, we have $\left[\begin{array}{l}\log _{2} x>2, \\ \log _{2} x4, \\ 0<x<\frac{1}{64}\end{array}\right.\right.$. Answer: $x \in\left(0 ; \frac{1}{64}\right) \cup(4 ; \infty)$.