# How do you solve e^x=5?

Jul 10, 2016

I found: $x = \ln 5$

#### Explanation:

You can apply the natural (base $e$) logarithm on both sides:
$\ln \left({e}^{x}\right) = \ln 5$
On the left the two operations will cancel out (one the inverse of the other) so you'll get:
$x = \ln 5$
If you can access a calculator (or tables) you can evaluate it as:
$x = \ln 5 = 1.6094$

Jul 19, 2018

$x = \ln 5$ or $\approx 1.609$

#### Explanation:

We want to cancel out base $e$. We can do this by taking the natural log of both sides.

$\ln {e}^{x} = \ln 5$

Since $\ln$ and $e$ are inverses of each other, they cancel, and we're left with

$x = \ln 5$

As a decimal, this is approximately $1.609$.

Hope this helps!