Answer
$3$ $log$ ${m}$ - $4$ $log$ ${n}$ + $2$ $log$ ${p}$
Work Step by Step
Use the Quotient Property of Logarithms. According to this property, $log_b$ ${m}$ - $log_b$ ${n}$ = $log_b$ $\frac {m}{n}$:
$log$ ${m^{3}}$ - $log$ ${n^{4}p^{-2}}$
Use the Product Property of Logarithms. According to this property, $log_b$ ${mn}$ = $log_b$ ${m}$ + $log_b$ ${n}$:
$log$ ${m^{3}}$ - ($log$ ${n^{4}}$ + $log$ ${p^{-2}})$
Use the Power Property of Logarithms to rewrite this expression. The property states that $log_b$ ${m^n}$ = $n$ $log_b$ ${m}$:
$3$ $log$ ${m}$ - ($4$ $log$ ${n}$ - $2$ $log$ ${p})$
Use distributive property:
$3$ $log$ ${m}$ - $4$ $log$ ${n}$ + $2$ $log$ ${p}$
