9.200. $\frac{\log _{0.5}(\sqrt{x+3}-1)}{\log _{0.5}(\sqrt{x+3}+5)}<\frac{1}{2}$.
## Solution.

Domain of definition: $\left\{\begin{array}{l}x+3 \geq 0, \\ \sqrt{x+3}>1,\end{array} \Leftrightarrow x>-2\right.$.

For $x>-2, \sqrt{x+3}+5>1$, therefore, $\log _{0.5}(\sqrt{x+3}+5)\log _{0.5}(\sqrt{x+3}+5) \Leftrightarrow$ $\Leftrightarrow\left\{\begin{array}{l}x>-2, \\ (\sqrt{x+3}-1)^{2}-2, \\ (\sqrt{x+3})^{2}-3 \sqrt{x+3}-41, \\ -1<\sqrt{x+3}<4\end{array} \Leftrightarrow 1<\sqrt{x+3}<4 \Leftrightarrow 1<x+3<16 \Leftrightarrow-2<x<13\right.$. Answer: $x \in(-2 ; 13)$.