Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Multiply $- 1$ by $1$ .

$\ln (1) - 1$

Step 6

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

$0 - 1$

Step 7

Subtract $1$ from $0$ .

$- 1$