Precalculus Examples

$\ln (5 e^{3})$

Step 1

Rewrite $\ln (5 e^{3})$ as $\ln (5) + \ln (e^{3})$ .

$\ln (5) + \ln (e^{3})$

Step 2

Use logarithm rules to move $3$ out of the exponent.

$\ln (5) + 3 \ln (e)$

Step 3

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

$\ln (5) + 3 \cdot 1$

Step 4

Multiply $3$ by $1$ .

$\ln (5) + 3$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\ln (5) + 3$

Decimal Form:

$4.60943791 \dots$