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

Jul 19, 2016

x = ± e

#### Explanation:

We can apply a property of logarithms, namely the property

$\ln \left(a\right) - \ln \left(b\right) = \ln \left(\frac{a}{b}\right)$

Thus, we have

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

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

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

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

x = ± e