Evaluate natural log of 6/e

$\ln (\frac{6}{e})$

Step 1

Rewrite $\frac{6}{e}$ as $6 e^{- 1}$ .

$\ln (6 e^{- 1})$

Step 2

Rewrite $\ln (6 e^{- 1})$ as $\ln (6) + \ln (e^{- 1})$ .

$\ln (6) + \ln (e^{- 1})$

Step 3

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

$\ln (6) - \ln (e)$

Step 4

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

$\ln (6) - 1 \cdot 1$

Step 5

Multiply $- 1$ by $1$ .

$\ln (6) - 1$

Step 6

Simplify each term.

Rewrite $\ln (6)$ as $\ln (2 (3))$ .

$\ln (2 (3)) - 1$

Rewrite $\ln (2 (3))$ as $\ln (2) + \ln (3)$ .

$\ln (2) + \ln (3) - 1$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\ln (2) + \ln (3) - 1$

Decimal Form:

$0.79175946 \dots$