# How do you use the properties of logarithms to rewrite(expand) each logarithmic expression log_b(yz^6))?

Mar 3, 2018

${\log}_{b} \left(y\right) + 6 {\log}_{b} \left(z\right)$

#### Explanation:

From the laws of logarithms:

$\textcolor{red}{\boldsymbol{\log \left(a b\right) = \log \left(a\right) + \log \left(b\right)}}$

$\textcolor{red}{\boldsymbol{\log \left({b}^{a}\right) = a \log \left(b\right)}}$

${\log}_{b} \left(y {z}^{6}\right) = {\log}_{b} \left(y\right) + {\log}_{b} \left({z}^{6}\right) \implies$

${\log}_{b} \left(y\right) + 6 {\log}_{b} \left(z\right)$