Precalculus Examples

$\log_{5} (\sqrt{5}) \cdot 5$

Multiply $\log_{5} (\sqrt{5}) \cdot 5$ .

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Reorder $\log_{5} (\sqrt{5})$ and $5$ .

$5 \cdot \log_{5} (\sqrt{5})$

Simplify $5 \cdot \log_{5} (\sqrt{5})$ by moving $5$ inside the logarithm.

$\log_{5} ({\sqrt{5}}^{5})$

Rewrite ${\sqrt{5}}^{5}$ as ${(5^{5})}^{\frac{1}{2}}$ .

$\log_{5} (\sqrt{5^{5}})$

Raise $5$ to the power of $5$ .

$\log_{5} (\sqrt{3125})$

Rewrite $3125$ as $25^{2} \cdot 5$ .

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Factor $625$ out of $3125$ .

$\log_{5} (\sqrt{625 (5)})$

Rewrite $625$ as $25^{2}$ .

$\log_{5} (\sqrt{25^{2} \cdot 5})$

Pull terms out from under the radical.

$\log_{5} (25 \sqrt{5})$

The result can be shown in multiple forms.

Exact Form:

$\log_{5} (25 \sqrt{5})$

Decimal Form:

$2.5$