Precalculus Examples

$x = \ln (\frac{1}{e})$

Step 1

Rewrite $\frac{1}{e}$ as $1 e^{- 1}$ .

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

Step 2

Rewrite $\ln (1 e^{- 1})$ as $\ln (1) + \ln (e^{- 1})$ .

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

Step 3

Use logarithm rules to move $- 1$ out of the exponent.

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

Step 4

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

$x = \ln (1) - 1 \cdot 1$

Step 5

Multiply $- 1$ by $1$ .

$x = \ln (1) - 1$

Step 6

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

$x = 0 - 1$

Step 7

Subtract $1$ from $0$ .

$x = - 1$