$9.283 \log _{x}^{2} \sqrt{5}-\log _{x} 5 \sqrt{5}+\frac{5}{4}<0$.

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$9.283 \log _{x}^{2} \sqrt{5}-\log _{x} 5 \sqrt{5}+\frac{5}{4}<0$.
Solution. The inequality is equivalent to the following:

$$
\begin{aligned}
& \frac{1}{4} \log _{x}^{2} 5-\frac{3}{2} \log _{x} 5+\frac{5}{4} \frac { 1 } { \log _ { 5 } x } , } \\
{ \frac { 1 } { \log _ { 5 } x } > 1 }
\end{aligned} \Leftrightarrow \left\{\begin{array} { l } 
{ \frac { 5 \log _ { 5 } x - 1 } { \log _ { 5 } x } > 0 , } \\
{ \frac { \log _ { 5 } x - 1 } { \log _ { 5 } x } \frac{1}{5},\right.} \\
\log _{5} x<0, \\
0<\log _{5} x<1
\end{array}\right.\right.\right.
\end{aligned}
$$

$\Leftrightarrow \frac{1}{5}<\log _{5} x<1 \Leftrightarrow 5^{\frac{1}{5}}<x<5$.

Answer: $\quad x \in(\sqrt[5]{5} ; 5)$.

$9.284\left|\log _{3} x\right|<\left|\log _{3} \frac{x}{9}\right|$.

Solution. $\left|\log _{3} x\right|<\mid \log _{3} x-2$ | Square both sides:

$\log _{3}^{2} x<\log _{3}^{2} x-4 \log _{3} x+4 \Leftrightarrow \log _{3} x<1 \Leftrightarrow 0<x<3$.

Answer: $x \in(0 ; 3)$.