# How do you use the properties of logarithms to expand lnxyz^2?

Jan 7, 2017

$\ln x + \ln y + 2 \ln z$

#### Explanation:

Since

$\log \left(a b\right) = \log a + \log b$,

then

$\ln \left(x y {z}^{2}\right) = \ln x + \ln y + \ln {z}^{2}$

and, since

$\log {a}^{b} = b \log a$

then the given expression is:

$\ln x + \ln y + 2 \ln z$