Precalculus Examples

$\log_{216} (\sqrt{36 \sqrt{6}})$

Step 1

Rewrite $36$ as $6^{2}$ .

$\log_{216} (\sqrt{6^{2} \sqrt{6}})$

Step 2

Pull terms out from under the radical.

$\log_{216} (6 \sqrt{\sqrt{6}})$

Step 3

Rewrite $\sqrt{\sqrt{6}}$ as $\sqrt[4]{6}$ .

$\log_{216} (6 \sqrt[4]{6})$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log_{216} (6 \sqrt[4]{6})$

Decimal Form:

$0.41\overline{6}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$