9.059. $4^{x}-2^{2(x-1)}+8^{\frac{2}{3}(x-2)}>52$.
## Solution.

## Given

$4^{x}-4^{x-1}+4^{x-2}>52, 4^{x}-\frac{4^{x}}{4}+\frac{4^{x}}{16}>52, 13 \cdot 4^{x}>16 \cdot 52$,

$4^{x}>4^{3} \Leftrightarrow x>3$.

Answer: $\quad x \in(3 ; \infty)$.