10. Solve the inequality $\log _{7}\left(\frac{1}{x^{2}-3}\right) \geq 0$.
Answer: $[-2,-\sqrt{3}) \cup(\sqrt{3}, 2]$
Solution: We need all values of $x$ such that $x^{2}-3>0$ and $\frac{1}{x^{2}-3} \geq 1$. The first has solution $(-\infty,-\sqrt{3}) \cup(3, \infty)$, while the second has solution $[-2,2]$. The intersection of these two sets is $[-2,-\sqrt{3}) \cup(\sqrt{3}, 2]$