How do you simplify $\frac{ln (e^{- 2 x})}{x}$ $ln(e^(-2x)) / x$ ?

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Answer 1 · 2016-08-20T21:00:14

This simplifies to $- 2$ $-2$

Start of by rewriting as follows

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

Using properties of logarithms we can rewrite the numerator

$\frac{ln | 1 | - ln ∣ ∣ e^{2 x} ∣ ∣}{x}$ $(ln|1|-ln|e^(2x)|)/x$

Remember $ln | 1 | = 0$ $ln|1|=0$

$\frac{0 - ln ∣ ∣ e^{2 x} ∣ ∣}{x}$ $(0-ln|e^(2x)|)/x$

Now rewrite the numerator again

$\frac{- 2 x ln | e |}{x}$ $(-2xln|e|)/x$

Remember $ln | e | = 1$ $ln|e|=1$

$\frac{- 2 x}{x} = - 2$ $(-2x)/x=-2$

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