# How do you solve 2 ln x = 1?

Mar 7, 2016

$x = \sqrt{e}$

#### Explanation:

Isolate the logarithm

$\ln \left(x\right) = \frac{1}{2}$

$\ln \left(x\right)$ is the natural logarithm, i.e.: it has base $e$, so take the exponential of both sides to get rid of the log

${e}^{\ln \left(x\right)} = {e}^{\frac{1}{2}}$
$x = {e}^{\frac{1}{2}}$

And there you go, if you prefer, you can remember that ${a}^{\frac{1}{2}} = \sqrt{a}$, so you can also rewrite that to

$x = \sqrt{e}$