Answer
$\displaystyle \frac{1}{2}\log_{a}(1+s)+\frac{1}{2}\log_{a}(1-s)$
Work Step by Step
Rewrite $\sqrt{1-s^{2}}$ as $(1-s^{2})^{1/2}$
$\log_{a}\sqrt{1-s^{2}}=\log_{a}(1-s^{2})^{1/2}\qquad$ ... apply $\log_{a}M^{p}=p\cdot\log_{a}M$
$=\displaystyle \frac{1}{2}\log_{a}(1-s^{2})\qquad$ ... recognize a difference of squares
$=\displaystyle \frac{1}{2}\log_{a}[(1+s)(1-s)]\qquad$ ... apply $\log_{a}(MN)=\log_{a}M+\log_{a}N$
$=\displaystyle \frac{1}{2}\log_{a}(1+s)+\frac{1}{2}\log_{a}(1-s)$
