7.199. $\log _{2} \log _{3}\left(x^{2}-16\right)-\log _{1 / 2} \log _{1 / 3} \frac{1}{x^{2}-16}=2$.
## Solution.

Domain of definition: $\log _{3}\left(x^{2}-16\right)>0 \Leftrightarrow x^{2}-16>3 \Leftrightarrow x^{2}>19 \Leftrightarrow$ $\Leftrightarrow x \in(-\infty ;-\sqrt{19}) \cup(\sqrt{19} ; \infty)$.

Rewrite the equation as

$\log _{2} \log _{3}\left(x^{2}-16\right)+\log _{2} \log _{3}\left(x^{2}-16\right)=2 \Leftrightarrow 2 \log _{2} \log _{3}\left(x^{2}-16\right)=2 \Leftrightarrow$ $\Leftrightarrow \log _{2} \log _{3}\left(x^{2}-16\right)=1$,

from which $\log _{3}\left(x^{2}-16\right)=2 \Leftrightarrow x^{2}-16=9, x^{2}=25$. We get $x_{1,2}= \pm 5$.

Answer: $-5 ; 5$.