Algebra Examples

$\log (\sqrt{2}) + \log (\sqrt{8})$

Step 1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log (\sqrt{2} \sqrt{8})$

Step 2

Combine using the product rule for radicals.

$\log (\sqrt{2 \cdot 8})$

Step 3

Simplify the expression.

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Step 3.1

Multiply $2$ by $8$ .

$\log (\sqrt{16})$

Step 3.2

Rewrite $16$ as $4^{2}$ .

$\log (\sqrt{4^{2}})$

Step 3.3

Pull terms out from under the radical, assuming positive real numbers.

$\log (4)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log (4)$

Decimal Form:

$0.60205999 \dots$