Finite Math Examples

$\log_{3} (\sqrt{243}) = x$

Step 1

Rewrite the equation as $x = \log_{3} (\sqrt{243})$ .

$x = \log_{3} (\sqrt{243})$

Step 2

Simplify $\log_{3} (\sqrt{243})$ .

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Step 2.1

Rewrite $243$ as $9^{2} \cdot 3$ .

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Step 2.1.1

Factor $81$ out of $243$ .

$x = \log_{3} (\sqrt{81 (3)})$

Step 2.1.2

Rewrite $81$ as $9^{2}$ .

$x = \log_{3} (\sqrt{9^{2} \cdot 3})$

Step 2.2

Pull terms out from under the radical.

$x = \log_{3} (9 \sqrt{3})$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \log_{3} (9 \sqrt{3})$

Decimal Form:

$x = 2.5$