# How do you solve ln(e^(7x)) = 15 ?

Mar 2, 2018

$x = \frac{15}{7}$

#### Explanation:

This is for natural logarithms.

$\ln \left({e}^{7 x}\right) = 15$

$\ln \left({a}^{b}\right) = b \ln \left(a\right)$

Then:

$\ln \left({e}^{7 x}\right) = 15$

$7 x \ln \left(e\right) = 15$

$\ln \left(e\right) = 1$ ( The logarithm of the base is always 1 )

$7 x = 15 \implies x = \frac{15}{7}$