# How do you solve ln x - ln (1/x) = 2?

Apr 27, 2018

$x = e$

#### Explanation:

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

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

or $\ln {x}^{2} = 2$

or $2 \ln x = 2$

or $\ln x = 1$

and $x = e$