9.070. $\log _{1.5} \frac{2 x-8}{x-2}<0$.
Solution.

The given inequality is equivalent to a system of two inequalities

$\left\{\begin{array}{l}\frac{2 x-8}{x-2}0\end{array} \Leftrightarrow\left\{\begin{array}{l}\frac{x-6}{x-2}0\end{array} \Leftrightarrow\left\{\begin{array}{l}(x-6)(x-2)0 .\end{array}\right.\right.\right.$

Using the number line, we get $x \in(4 ; 6)$.

![](https://cdn.mathpix.com/cropped/2024_05_22_fa9db84b44b98ec0a5c7g-542.jpg?height=132&width=612&top_left_y=1210&top_left_x=254)

Answer: $\quad x \in(4 ; 6)$