Precalculus Examples

$\frac{\log_{81} (27) \cdot 3}{7}$

Step 1

Simplify the numerator.

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Step 1.1

Reorder $\log_{81} (27)$ and $3$ .

$\frac{3 \cdot \log_{81} (27)}{7}$

Step 1.2

Simplify $3 \cdot \log_{81} (27)$ by moving $3$ inside the logarithm.

$\frac{\log_{81} (27^{3})}{7}$

Step 2

Simplify the numerator.

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Step 2.1

Raise $27$ to the power of $3$ .

$\frac{\log_{81} (19683)}{7}$

Step 2.2

Logarithm base $81$ of $19683$ is $\frac{9}{4}$ .

$\frac{\frac{9}{4}}{7}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{9}{4} \cdot \frac{1}{7}$

Step 4

Multiply $\frac{9}{4} \cdot \frac{1}{7}$ .

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Step 4.1

Multiply $\frac{9}{4}$ by $\frac{1}{7}$ .

$\frac{9}{4 \cdot 7}$

Step 4.2

Multiply $4$ by $7$ .

$\frac{9}{28}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{28}$

Decimal Form:

$0.32142857 \dots$