Precalculus Examples

$\log_{3} (27^{3 x + 7} \cdot 81^{3 x + 7})$

Step 1

Multiply $27^{3 x + 7} \cdot 81^{3 x + 7}$ .

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Step 1.1

Rewrite $27^{3 x + 7} \cdot 81^{3 x + 7}$ as ${(27 \cdot 81)}^{3 x + 7}$ .

$\log_{3} ({(27 \cdot 81)}^{3 x + 7})$

Step 1.2

Multiply $27$ by $81$ .

$\log_{3} (2187^{3 x + 7})$

Step 2

Rewrite $\log_{3} (2187^{3 x + 7})$ using the change of base formula.

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Step 2.1

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 2.2

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

$\frac{\log (2187^{3 x + 7})}{\log (3)}$