# How do you simplify ln(e^(-2x)) / x?

Aug 20, 2016

This simplifies to $- 2$

#### Explanation:

Start of by rewriting as follows

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

Using properties of logarithms we can rewrite the numerator

$\frac{\ln | 1 | - \ln | {e}^{2 x} |}{x}$

Remember $\ln | 1 | = 0$

$\frac{0 - \ln | {e}^{2 x} |}{x}$

Now rewrite the numerator again

$\frac{- 2 x \ln | e |}{x}$

Remember $\ln | e | = 1$

$\frac{- 2 x}{x} = - 2$