Precalculus Examples

$\log ({(\sqrt{3})}^{9})$

Step 1

Rewrite ${\sqrt{3}}^{9}$ as $\sqrt{3^{9}}$ .

$\log (\sqrt{3^{9}})$

Step 2

Raise $3$ to the power of $9$ .

$\log (\sqrt{19683})$

Step 3

Rewrite $19683$ as $81^{2} \cdot 3$ .

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Step 3.1

Factor $6561$ out of $19683$ .

$\log (\sqrt{6561 (3)})$

Step 3.2

Rewrite $6561$ as $81^{2}$ .

$\log (\sqrt{81^{2} \cdot 3})$

$\log (\sqrt{81^{2} \cdot 3})$

Step 4

Pull terms out from under the radical.

$\log (81 \sqrt{3})$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log (81 \sqrt{3})$

Decimal Form:

$2.14704564 \dots$

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