Precalculus Examples

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

Step 1

Rewrite $\frac{1}{e^{5 x}}$ as ${(e^{5 x})}^{- 1}$ .

$\ln ({(e^{5 x})}^{- 1})$

Step 2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\ln (e^{5 x \cdot - 1})$

Step 3

Use logarithm rules to move $5 x \cdot - 1$ out of the exponent.

$5 x \cdot - 1 \ln (e)$

Step 4

Multiply $- 1$ by $5$ .

$- 5 x \ln (e)$

Step 5

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

$- 5 x \cdot 1$

Step 6

Multiply $- 5$ by $1$ .

$- 5 x$