Precalculus Examples

$\log_{25} (\sqrt[8]{5^{3}})$

Step 1

Raise $5$ to the power of $3$ .

$\log_{25} (\sqrt[8]{125})$

Step 2

Rewrite $\log_{25} (\sqrt[8]{125})$ using the change of base formula.

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Step 2.1

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 2.2

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

$\frac{\log (\sqrt[8]{125})}{\log (25)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (\sqrt[8]{125})}{\log (25)}$

Decimal Form:

$0.1875$