## Precalculus: Mathematics for Calculus, 7th Edition

$\frac{1}{2}$$\ln a + \frac{1}{2}$$\ln b$
$Expand$ $the$ $expression$: $\ln \sqrt{ab}$ 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$