$9.271 \log _{1 / 2}(x-3)-\log _{1 / 2}(x+3)-\log _{\frac{x+3}{x-3}} 2>0$.

Translate the text above into English, keeping the original text's line breaks and format, and output the translation result directly.

$9.271 \log _{1 / 2}(x-3)-\log _{1 / 2}(x+3)-\log _{\frac{x+3}{x-3}} 2>0$.
Solution. The original inequality is equivalent to the system:

$$
\left\{\begin{array} { l } 
{ \operatorname { log } _ { 2 } \frac { x + 3 } { x - 3 } - \operatorname { log } _ { \frac { x + 3 } { x - 3 } } 2 > 0 } \\
{ x > 3 }
\end{array} \Leftrightarrow \left\{\begin{array}{l}
\frac{\log _{2}^{2} \frac{x+3}{x-3}-1}{\log _{2} \frac{x+3}{x-3}}>0 \\
x>3
\end{array}\right.\right.
$$

Let $y=\log _{2} \frac{x+3}{x-3}$, then

$$
\left\{\begin{array} { l } 
{ \frac { ( y - 1 ) ( y + 1 ) } { y } > 0 , } \\
{ x > 3 }
\end{array} \Leftrightarrow \left\{\begin{array} { l } 
{ [ \begin{array} { l } 
{ y > 1 } \\
{ - 1 < y < 0 } 
\end{array} } \\
{ x > 3 }
\end{array} \Leftrightarrow \left\{\begin{array}{l}
{\left[\begin{array}{l}
\log _{2} \frac{x+3}{x-3}>1 \\
-1 < \log _{2} \frac{x+3}{x-3} < 0
\end{array} \Leftrightarrow\right.\right.\right.
$$

$\Leftrightarrow\left\{\begin{array}{l}{\left[\begin{array}{l}\frac{x+3}{x-3}>2, \\ \frac{1}{2} < \frac{x+3}{x-3} < 1\end{array} \Leftrightarrow\left\{\begin{array}{l}{\left[\begin{array}{l}x>9 \\ 3 < x < 9\end{array}\right.}\end{array} \Leftrightarrow 3 < x < 9\right.\right.\right.$.

Answer: $x \in(3 ; 9)$.

$9.272\left|2^{4 x^{2}-1}-5\right| \leq 3$.

Solution: $-3 \leq 2^{4 x^{2}-1}-5 \leq 3 \Leftrightarrow 2^{1} \leq 2^{4 x^{2}-1} \leq 2^{3} \Leftrightarrow 1 \leq 4 x^{2}-1 \leq 3 \Leftrightarrow$ $\Leftrightarrow \frac{1}{2} \leq x^{2} \leq 1 \Leftrightarrow \frac{1}{\sqrt{2}} \leq|x| \leq 1$.

Answer: $\quad x \in\left[-1 ;-\frac{1}{\sqrt{2}}\right] \cup\left[\frac{1}{\sqrt{2}} ; 1\right]$.