Evaluate log base 15 of 2^3

$\log_{15} (2^{3})$

Raise $2$ to the power of $3$ .

$\log_{15} (8)$

Rewrite $\log_{15} (8)$ using the change of base formula.

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 $b = 10$ .

$\frac{\log (8)}{\log (15)}$

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (8)}{\log (15)}$

Decimal Form:

$0.76787407 \dots$