# How do you calculate  log_32 64?

Apr 9, 2016

$\frac{6}{5}$

#### Explanation:

First you should see that
$64 = {2}^{6}$
$32 = {2}^{5}$

Then it's convenient to convert the ${\log}_{32}$ to ${\log}_{2}$ using this property
${\log}_{a}^{b} = {\log}_{c}^{b} / {\log}_{c}^{a}$

So
${\log}_{32}^{64} = {\log}_{2}^{64} / \left({\log}_{2}^{32}\right) = {\log}_{2}^{{2}^{6}} / \left({\log}_{2}^{{2}^{5}}\right) = \frac{6}{5}$