# How do you solve 10 = e ^ x?

Dec 15, 2015

$x = \ln \left(10\right)$

#### Explanation:

To get rid of the base $e$, we can take the natural log of both sides:

$10 = {e}^{x} \to \ln \left(10\right) = \ln \left({e}^{x}\right) \to x = \ln \left(10\right)$

This value is irrational, so the only exact way to write it is $\ln \left(10\right)$.

Dec 15, 2015

I found: $x = 2.3025$

#### Explanation:

One way is to take the natural log of both sides (which can be evaluated using a pocket calculator) to get:
$\ln 10 = \ln {e}^{x}$
where from the definition of log:
$\ln {e}^{x} = x$
so:
$x = \ln 10 = 2.3025$

Dec 15, 2015

Take the natural log of both sides of the equation ...

#### Explanation:

$\ln 10 = \ln \left({e}^{x}\right)$

Now, simplify and solve for x ...

$\ln 10 = x$

$x \approx 2.3026$

Verify ...

${e}^{2.3026} = 10.000$

hope that helped