Precalculus Examples

$\log_{5} (\sqrt{125}) - \log_{2} (\sqrt{2})$

Step 1

Rewrite $125$ as $5^{2} \cdot 5$ .

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Step 1.1

Factor $25$ out of $125$ .

$\log_{5} (\sqrt{25 (5)}) - \log_{2} (\sqrt{2})$

Step 1.2

Rewrite $25$ as $5^{2}$ .

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

Step 2

Pull terms out from under the radical.

$\log_{5} (5 \sqrt{5}) - \log_{2} (\sqrt{2})$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\log_{5} (5 \sqrt{5}) - \log_{2} (\sqrt{2})$

Decimal Form:

$1$