9.054. $5^{2 x+1}>5^{x}+4$.

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9.054. $5^{2 x+1}>5^{x}+4$.
Solution.

We have $5 \cdot\left(5^{x}\right)^{2}-\left(5^{x}\right)+4>0$. Solving it as a quadratic equation in terms of $5^{x}$, we get $5^{x} > 1$, from which $x > 0$.

Answer: $\quad x \in (0 ; \infty)$