# If ln x - ln (1/x) = 2, then how do you find x?

Oct 25, 2016

$x = e$

#### Explanation:

We use the rule $\ln a - \ln b = \ln \left(\frac{a}{b}\right)$ to start the solving process.

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

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

If $\ln a = b$, ${e}^{b} = a$

${x}^{2} = {e}^{2}$

$x = \pm \sqrt{{e}^{2}}$

$x = \pm e$

However, the negative answer is not possible as it renders the original equation undefined.

Hopefully this helps!