Precalculus Examples

$\ln (5 e^{4})$

Step 1

Rewrite $\ln (5 e^{4})$ as $\ln (5) + \ln (e^{4})$ .

$\ln (5) + \ln (e^{4})$

Step 2

Use logarithm rules to move $4$ out of the exponent.

$\ln (5) + 4 \ln (e)$

Step 3

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

$\ln (5) + 4 \cdot 1$

Step 4

Multiply $4$ by $1$ .

$\ln (5) + 4$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\ln (5) + 4$

Decimal Form:

$5.60943791 \dots$