Answer
$1$ + $4$ $log$ ${m}$ + $2$ $log$ ${n}$
Work Step by Step
Use the Product Property of Logarithms. According to this property, $log_b$ ${mn}$ = $log_b$ ${m}$ + $log_b$ ${n}$:
$log$ ${10}$ + $log$ ${m^{4}}$ + $log$ ${n^{2}}$
Use the Power Property of Logarithms to rewrite this expression. The property states that $log_b$ ${m^n}$ = $n$ $log_b$ ${m}$:
$log$ ${10}$ + $4$ $log$ ${m}$ + $2$ $log$ ${n}$
Use the logarithmic identity $log_{b}$ ${b}$ = $1$:
$1$ + $4$ $log$ ${m}$ + $2$ $log$ ${n}$