# How do you expand this logarithm?

## ${\log}_{9} \left(z \sqrt{x} \cdot y\right)$

Nov 26, 2016

This is the best I got...

#### Explanation:

Try to use the product of the arguments to change it into a sum of logs as:
${\log}_{9} \left(z \sqrt{x} \cdot y\right) = {\log}_{9} \left(z \cdot \sqrt{x}\right) + {\log}_{9} \left(y\right) =$ and again:
$= {\log}_{9} \left(z\right) + {\log}_{9} \left(\sqrt{x}\right) + {\log}_{9} \left(y\right)$

Nov 27, 2016

${\log}_{9} \sqrt{x} = {\log}_{9} {x}^{\frac{1}{2}} = \frac{1}{2} {\log}_{9} x$