G4.4 Let $Q=\log _{2+\sqrt{2^{2}-1}}\left(2-\sqrt{2^{2}-1}\right)$, find the value of $Q$.
$\begin{array}{l}Q=\frac{\log (2-\sqrt{3})}{\log (2+\sqrt{3})} \\ =\frac{\log (2-\sqrt{3})}{\log (2+\sqrt{3}) \cdot \frac{(2-\sqrt{3}}{(2-\sqrt{3})}} \\ =\frac{\log (2-\sqrt{3})}{\log \frac{1}{2-\sqrt{3}}} \\ =\frac{\log (2-\sqrt{3})}{-\log (2-\sqrt{3})}=-1 \\ \text { Method } 2 Q=\log _{2+\sqrt{3}}(2-\sqrt{3}) \cdot \frac{(2+\sqrt{3})}{(2+\sqrt{3})} \\ =\log _{2+\sqrt{3}} \frac{1}{(2+\sqrt{3})} \\ =\log _{2+\sqrt{3}}(2+\sqrt{3})^{-1}=-1 \\\end{array}$