Evaluate log base 8 of square root of 5

$\log_{8} (\sqrt{5})$

Step 1

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 $0$ .

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

Step 2

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

$\frac{\log (\sqrt{5})}{\log (8)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (\sqrt{5})}{\log (8)}$

Decimal Form:

$0.38698801 \dots$