# How do you change (1/5)^4 = 1/625 into log form?

Jul 15, 2016

$4 \ln \left(5\right) = \ln \left(625\right)$

#### Explanation:

if by log form you are referring to the natural logarithm then you apply the function as such

$\ln \left({\left(\frac{1}{5}\right)}^{4}\right) = \ln \left(\frac{1}{625}\right)$

$4 \ln \left(\frac{1}{5}\right) = \ln \left(\frac{1}{625}\right)$

$4 \ln \left(1\right) - 4 \ln \left(5\right) = \ln \left(1\right) - \ln \left(625\right)$
technically the log of anything that is 1 is 0
$- 4 \ln \left(5\right) = - \ln \left(625\right)$
$4 \ln \left(5\right) = \ln \left(625\right)$