Calculus Examples

$\ln (\sqrt[3]{e^{4}})$

Step 1

Factor out $e^{3}$ .

$\ln (\sqrt[3]{e^{3} e})$

Step 2

Pull terms out from under the radical.

$\ln (e \sqrt[3]{e})$

Step 3

Rewrite $\ln (e \sqrt[3]{e})$ as $\ln (e) + \ln (\sqrt[3]{e})$ .

$\ln (e) + \ln (\sqrt[3]{e})$

Step 4

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

$1 + \ln (\sqrt[3]{e})$

Step 5

The result can be shown in multiple forms.

Exact Form:

$1 + \ln (\sqrt[3]{e})$

Decimal Form:

$1.\overline{3}$