Precalculus Examples

$g \log_{g} (30)$

Step 1

Rewrite $\log_{g} (30)$ using the change of base formula.

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Step 1.1

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 $0$ .

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

Step 1.2

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

$g \frac{\log (30)}{\log (g)}$

Step 2

Combine $g$ and $\frac{\log (30)}{\log (g)}$ .

$\frac{g \log (30)}{\log (g)}$