Precalculus Examples

$\log_{5} (3 \cdot 2)$

Step 1

Multiply $3$ by $2$ .

$\log_{5} (6)$

Step 2

Rewrite $\log_{5} (6)$ using the change of base formula.

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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 $b = 10$ .

$\frac{\log (6)}{\log (5)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (6)}{\log (5)}$

Decimal Form:

$1.11328275 \dots$