9.128. $y=\log _{3}\left(2^{\log _{x-3} 0.5}-1\right)+\frac{1}{\log _{3}(2 x-6)}$.
## Solution.

The domain of the given function will be found by solving the system of inequalities

$$
\left\{\begin{array} { l } 
{ 2 ^ { \operatorname { log } _ { x - 3 } 0.5 } - 1 > 0 , } \\
{ \operatorname { log } _ { 3 } ( 2 x - 6 ) \neq 0 , } \\
{ 2 x - 6 > 0 }
\end{array} \Leftrightarrow \left\{\begin{array} { l } 
{ 2 ^ { \operatorname { log } _ { x - 3 } 0.5 } > 1 , } \\
{ 2 x - 6 \neq 1 , } \\
{ 2 x - 6 > 0 }
\end{array} \Leftrightarrow \left\{\begin{array}{l}
\log _{x-3} 0.5>0 \\
2 x \neq 7 \\
2 x>6
\end{array}\right.\right.\right.
$$

We get two cases:

1) $\left\{\begin{array}{l}03\end{array}\right.$
2) $\left\{\begin{array}{l}31, \\ & 0.5>1, \\ & x \neq \frac{7}{2}, \\ & x>3,\end{aligned}$

Answer: $x \in\left(3 ; \frac{7}{2}\right) \cup\left(\frac{7}{2} ; 4\right)$.