How to express $\log_2 (\sqrt{9} - \sqrt{5})$ in terms of $k=\log_2 (\sqrt{9} + \sqrt{5})$? If $$k=\log_2 (\sqrt{9} + \sqrt{5})$$
express $\log_2 (\sqrt{9} - \sqrt{5})$ in terms of $k$. 

Add to both sides the term $\log_2 (\sqrt{9} - \sqrt{5})$, then you have
$$
\log_2 (\sqrt{9} - \sqrt{5}) + k = \log_2 (4),
$$
so that
$$
\log_2 (\sqrt{9} - \sqrt{5}) = 2 - k. 
$$
