Answer
$\frac{1}{2}$$\ln a$ + $\frac{1}{2}$$\ln b$
Work Step by Step
$Expand$ $the$ $expression$:
$\ln \sqrt{ab}$
Rewrite the root to exponential form
$\ln (ab)^{\frac{1}{2}}$
Apply the Third Law of Logarithms
$\ln (ab)^{\frac{1}{2}}$ = $\frac{1}{2}$$\ln ab$
Apply the First Law of Logarithms and distribute the half to both terms
$\frac{1}{2}$$\ln (a \times b)$ = $\frac{1}{2}$$\ln a$ + $\frac{1}{2}$$\ln b$