# How do you write 32=x^5 in Logarithm form?

Aug 28, 2016

$32 = {x}^{5} \iff 5 = {\log}_{x} 32$.

Aug 28, 2016

It can be written:

${\log}_{x} 32 = 5 \text{ }$ or $\text{ } {\log}_{32} x = \frac{1}{5}$

#### Explanation:

Given:

$32 = {x}^{5}$

If we take logs base $x$ we find:

${\log}_{x} 32 = {\log}_{x} {x}^{5} = 5$

Alternatively, if we take logs base $32$ we find:

$1 = {\log}_{32} 32 = {\log}_{32} {x}^{5} = 5 {\log}_{32} x$

Hence:

${\log}_{32} x = \frac{1}{5}$