Evaluate natural log of sixth root of e^4

$\ln (\sqrt[6]{e^{4}})$

Step 1

Rewrite $e^{4}$ as ${(e^{2})}^{2}$ .

$\ln (\sqrt[6]{{(e^{2})}^{2}})$

Step 2

Rewrite $\sqrt[6]{{(e^{2})}^{2}}$ as $\sqrt[3]{\sqrt{{(e^{2})}^{2}}}$ .

$\ln (\sqrt[3]{\sqrt{{(e^{2})}^{2}}})$

Step 3

Pull terms out from under the radical, assuming positive real numbers.

$\ln (\sqrt[3]{e^{2}})$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\ln (\sqrt[3]{e^{2}})$

Decimal Form:

$0.\overline{6}$