Algebra Examples

$\log_{3} (a) \cdot \log (3)$

Step 1

Rewrite $\log_{3} (a)$ 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 $0$ .

$\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)} \log (3)$

Step 1.2

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

$\frac{\log (a)}{\log (3)} \log (3)$

Step 2

Cancel the common factor of $\log (3)$ .

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Step 2.1

Cancel the common factor.

$\frac{\log (a)}{\log (3)} \log (3)$

Step 2.2

Rewrite the expression.

$\log (a)$