# How do you solve 5ln x = 35?

Dec 21, 2015

$x = {e}^{7}$

#### Explanation:

Divide both sides by $5$.

$\ln x = 7$

Undo the natural logarithm by exponentiating both sides.

${e}^{\ln x} = {e}^{7}$

$x = {e}^{7}$

This could also be solved by rewriting $5 \ln x$ using logarithm rules.

$\ln \left({x}^{5}\right) = 35$

${e}^{\ln \left({x}^{5}\right)} = {e}^{35}$

${x}^{5} = {e}^{35}$

${\left({x}^{5}\right)}^{\frac{1}{5}} = {\left({e}^{35}\right)}^{\frac{1}{5}}$

$x = {e}^{7}$