Precalculus Examples

$\log_{3} (9^{2} \cdot 5^{4})$

Step 1

Raise $9$ to the power of $2$ .

$\log_{3} (81 \cdot 5^{4})$

Step 2

Raise $5$ to the power of $4$ .

$\log_{3} (81 \cdot 625)$

Step 3

Multiply $81$ by $625$ .

$\log_{3} (50625)$

Step 4

Rewrite $\log_{3} (50625)$ 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 $b = 10$ .

$\frac{\log (50625)}{\log (3)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (50625)}{\log (3)}$

Decimal Form:

$9.85989408 \dots$