$9.268 \log _{|x-4|}\left(2 x^{2}-9 x+4\right)>1$.

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$9.268 \log _{|x-4|}\left(2 x^{2}-9 x+4\right)>1$.
Solution. $\log _{\mid x-4}\left(2 x^{2}-9 x+4\right)>\log _{\mid x-4}|x-4|$.

1) $\left\{\begin{array}{l}|x-4|>1, \\ 2 x^{2}-9 x+4>|x-4|\end{array} \Leftrightarrow\left\{\begin{array}{l}{\left[\begin{array}{l}x5, \\ x-4-2 x^{2}+9 x-4\end{array}\right.}\end{array} \Leftrightarrow\left\{\begin{array}{l}{\left[\begin{array}{l}x>5, \\ x4, \\ x4, \\ x5 .\end{array}\right.\right.\right.\right.$
2) $\left\{\begin{array}{l}00\end{array}, \Leftrightarrow\left\{\begin{array}{l}x \neq 4, \\ 34\end{array}\right.}\end{array} \Leftrightarrow\left\{\begin{array}{l}4<x<5, \\ 2 x^{2}-9 x+4<x-4\end{array} \Leftrightarrow \varnothing\right.\right.\right.$.

Answer: $x \in(-\infty ; 0) \cup(3 ;+\infty)$.