Chapter 7 - Exponential and Logarithmic Functions - 7-4 Properties of Logarithms - Practice and Problem-Solving Exercises - Page 466: 29

$1$ + $4$ $log$ ${m}$ + $2$ $log$ ${n}$

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 $log_{b}$ ${b}$ = $1$: $1$ + $4$ $log$ ${m}$ + $2$ $log$ ${n}$