# How do you use the properties of logarithms to expand log_8 (x^4)?

Jun 25, 2017

$4 {\log}_{8} \left(x\right)$

#### Explanation:

To expand this logarithm, the first thing we can do is change the ${x}^{4}$:

${\log}_{8} \left({x}^{4}\right)$

The argument is, which in this case is ${x}^{4}$, can be rewritten. We can move the "power of four" to the front of the expression, using the third property of logarithims, which states ${\log}_{a} {u}^{\textcolor{red}{n}} = \textcolor{red}{n} {\log}_{a} u$

Using that property, we get

$4 {\log}_{8} \left(x\right)$

Jun 25, 2017

$4 {\log}_{8} x$
$\text{using the "color(blue)"law of logarithms}$
• logx^nhArrnlogx
$\Rightarrow {\log}_{8} {x}^{4} = 4 {\log}_{8} x$