Question

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

Answer 1

This simplifies to `-2`

Explanation:

Start of by rewriting as follows

`ln(1/e^(2x))/x`

Using properties of logarithms we can rewrite the numerator

`(ln|1|-ln|e^(2x)|)/x`

Remember `ln|1|=0`

`(0-ln|e^(2x)|)/x`

Now rewrite the numerator again

`(-2xln|e|)/x`

Remember `ln|e|=1`

`(-2x)/x=-2`