Evaluate log base 5 of square root of 5

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

The change of base rule can be used if $a$ and $b$ are greater than $0$ and not equal to $1$ , and $x$ is greater than $0$ .

$\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}$

Substitute in values for the variables in the change of base formula, using $b = 10$ .

$\frac{\log (\sqrt{5})}{\log (5)}$

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (\sqrt{5})}{\log (5)}$

Decimal Form:

$0.5$