# How do you solve 5*e^(2n)=56.7?

Jun 26, 2017

I got: $n = \frac{1}{2} \ln \left(11.34\right) = 1.214168$

#### Explanation:

We can rearrange it:
${e}^{2 n} = \frac{56.7}{5}$
${e}^{2 n} = 11.34$
apply the natural log to both sides:
$\ln \left[{e}^{2 n}\right] = \ln \left(11.34\right)$
use a property of logs:
$2 n \ln \left(e\right) = \ln \left(11.34\right)$
and then:
$2 n = \ln \left(11.34\right)$
$n = \frac{1}{2} \ln \left(11.34\right) = 1.214168$