Answer
$\ln (\frac{a^2-b^2}{c^2}$)
Work Step by Step
$Combine$ $the$ $expression$:
$\ln (a+b)$ + $\ln (a-b)$ - $2$$\ln c$
Apply the Third Law of Logarithms for $2$$\ln c$
$2$$\ln c$ = $\ln c^2$
$\ln (a+b)$ + $\ln (a-b)$ - $\ln c^2$
Apply the First Law of Logarithms for $\ln (a+b)$ + $\ln (a-b)$
$\ln (a+b)$ + $\ln (a-b)$ = $\ln ((a+b)(a-b))$ [Note: Use FOIL Method]
$\ln (a^2-ab+ab-b^2)$ = $\ln (a^2-b^2)$
$\ln (a^2-b^2)$ - $\ln c^2$
Apply the Second Law of Logarithms
$\ln (a^2-b^2)$ - $\ln c^2$ = $\ln (\frac{a^2-b^2}{c^2}$)