$9.279 \log _{x} 10-0.5 \log _{a} 10>0, \ 0<a<1$.
## Solution.

$\log _{x} 10>\frac{1}{\log _{10} a^{2}} \Leftrightarrow \frac{\lg a^{2}}{\lg x}\lg x\end{array} \Leftrightarrow\left\{\begin{array}{l}0<x<1, \\ \lg a^{2}<0, \\ 0<x<a^{2}\end{array} \text { or } \left\{\begin{array}{l}x>1, \\ \lg a^{2}>0, \\ x>a^{2}\end{array} \Leftrightarrow x>1\right.\right.$.

Answer: $\quad x \in\left(0 ; a^{2}\right) \cup(1 ;+\infty)$.