Precalculus Examples

$32^{\log_{2} (3)}$

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 $0$ .

$32^{\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}}$

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

$32^{\frac{\log (3)}{\log (2)}}$

The result can be shown in multiple forms.

Exact Form:

$32^{\frac{\log (3)}{\log (2)}}$

Decimal Form:

$243$