# If 17^m=6, what is m?

Jun 26, 2017

$m = \ln \frac{6}{\ln} \left(17\right)$

#### Explanation:

Given ${17}^{m} = 6$

Use the natural logarithm on both sides:

$\ln \left({17}^{m}\right) = \ln \left(6\right)$

NOTE: You can use any base logarithm you like; I have arbitrarily chosen natural logarithms.

Use the property of logarithms $\ln \left({a}^{c}\right) = c \ln \left(a\right)$:

$m \ln \left(17\right) = \ln \left(6\right)$

Divide both sides by $\ln \left(17\right)$

$m = \ln \frac{6}{\ln} \left(17\right)$