Simplify/Condense log of square root of 2+ log of square root of 8

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

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

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

Combine using the product rule for radicals.

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

Simplify the expression.

Multiply $2$ by $8$ .

$\log (\sqrt{16})$

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

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

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

$\log (4)$

The result can be shown in multiple forms.

Exact Form:

$\log (4)$

Decimal Form:

$0.60205999 \dots$