Precalculus Examples

$\log_{3} (6^{3} \cdot 9^{6})$

Step 1

Raise $6$ to the power of $3$ .

$\log_{3} (216 \cdot 9^{6})$

Step 2

Raise $9$ to the power of $6$ .

$\log_{3} (216 \cdot 531441)$

Step 3

Multiply $216$ by $531441$ .

$\log_{3} (114791256)$

Step 4

Rewrite $\log_{3} (114791256)$ using the change of base formula.

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Step 4.1

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 4.2

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

$\frac{\log (114791256)}{\log (3)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (114791256)}{\log (3)}$

Decimal Form:

$16.89278926 \dots$