# How do you solve e^(-3n)=83?

May 9, 2017

Take the natural log of both sides and solve.

#### Explanation:

Note that $\ln \left(x\right)$ is the natural logarithm or ${\log}_{e} \left(x\right)$.

First, we can take the natural log of both sides to get $n$ out of the exponent:
$\ln \left({e}^{- 3 n}\right) = \ln \left(83\right)$

Since the $\ln$ and the $e$ cancel, we get:
$- 3 n = \ln \left(83\right)$

Dividing $- 3$ from both sides, we get our value of $n$ as:
$n = - \ln \frac{83}{3} \approx - 1.473$ rounded to three decimal places