Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

The natural logarithm of $1$ is $0$ .

$0 - (5 x \ln (e))$

Step 4

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

$0 - (5 x \cdot 1)$

Step 5

Subtract $5 x \cdot 1$ from $0$ .

$- (5 x \cdot 1)$

Step 6

Multiply $5$ by $1$ .

$- (5 x)$

Step 7

Multiply $5$ by $- 1$ .

$- 5 x$