Evaluate natural log of 1/(e^5)

$\ln (\frac{1}{e^{5}})$

Step 1

Move $e^{5}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$\ln (e^{- 5})$

Step 2

Expand $\ln (e^{- 5})$ by moving $- 5$ outside the logarithm.

$- 5 \ln (e)$

Step 3

The natural logarithm of $e$ is $1$ .

$- 5 \cdot 1$

Step 4

Multiply $- 5$ by $1$ .

$- 5$