# How do you solve 3e^x=122?

Jun 9, 2016

Using the logarithm.

#### Explanation:

The way to "pull down" the $x$ from an exponential is to use the inverse function that is the logarithm.

$3 {e}^{x} = 122$

${e}^{x} = \frac{122}{3}$

Then we apply the logarithm on both sides

$\ln \left({e}^{x}\right) = \ln \left(\frac{122}{3}\right)$

Because the logarithm is the inverse of the exponential, they cancel each other on the left

$x = \ln \left(\frac{122}{3}\right) \setminus \approx 3.7$.