9.204. $\log _{3}\left(\log _{2}\left(2-\log _{4} x\right)-1\right)<1$.
## Solution.

The given inequality is equivalent to the double inequality

$$
\begin{aligned}
& 0<\log _{2}\left(2-\log _{4} x\right)-1<3 \Leftrightarrow 1<\log _{2}\left(2-\log _{4} x\right)<4 \Leftrightarrow \\
& \Leftrightarrow 2<2-\log _{4} x<16,0<-\log _{4} x<14 \Leftrightarrow-14<\log _{4} x<0, \\
& \frac{1}{4^{14}}<x<1,2^{-28}<x<1 . \\
& \text { Answer: } x \in\left(2^{-28} ; 1\right) .
\end{aligned}
$$