9.166. $3^{\lg x+2}<3^{\lg x^{2}+5}-2$.

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9.166. $3^{\lg x+2}<3^{\lg x^{2}+5}-2$.
## Solution.

Domain of definition: $x>0$.

Let's write the given inequality as $243 \cdot\left(3^{\lg x}\right)^{2}-9 \cdot 3^{\lg x}-2>0$. Solving 

it as a quadratic equation in terms of $3^{\lg x}$, we find $\left[\begin{array}{l}3^{\lg x}>3^{-2}, \\ 3^{\lg x}-2, x>0.01\end{array}\right.$.

Answer: $x \in(0.01 ; \infty)$.