# How do you evaluate 10 log18 - log3?

##### 1 Answer
Dec 21, 2015

$10 \log \left(18\right) - \log \left(3\right) = \log \left({18}^{10} / 3\right)$

#### Explanation:

Remember

1. $m \log \left(n\right) = \log \left({n}^{m}\right)$
2. $\log \left(a\right) - \log \left(b\right) = \log \left(\frac{a}{b}\right)$

Therefore
$\textcolor{w h i t e}{\text{XXX}} 10 \log \left(18\right) - \log \left(3\right)$

$\textcolor{w h i t e}{\text{XXX}} = \log \left({18}^{10}\right) - \log \left(3\right)$

$\textcolor{w h i t e}{\text{XXX}} = \log \left({18}^{10} / 3\right)$

This could be evaluated using a calculator as:
$\textcolor{w h i t e}{\text{XXX}} = 12.0756$