Precalculus Examples

$\log_{9} ({(\frac{3^{3}}{7})}^{4})$

Step 1

Expand $\log_{9} ({(\frac{3^{3}}{7})}^{4})$ by moving $4$ outside the logarithm.

$4 \log_{9} (\frac{3^{3}}{7})$

Step 2

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

$4 \log_{9} (\frac{27}{7})$

Step 3

Rewrite $\log_{9} (\frac{27}{7})$ as $\log_{9} (27) - \log_{9} (7)$ .

$4 (\log_{9} (27) - \log_{9} (7))$

Step 4

Logarithm base $9$ of $27$ is $\frac{3}{2}$ .

$4 (\frac{3}{2} - \log_{9} (7))$

Step 5

Apply the distributive property.

$4 (\frac{3}{2}) + 4 (- \log_{9} (7))$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Factor $2$ out of $4$ .

$2 (2) \frac{3}{2} + 4 (- \log_{9} (7))$

Step 6.2

Cancel the common factor.

$2 \cdot 2 \frac{3}{2} + 4 (- \log_{9} (7))$

Step 6.3

Rewrite the expression.

$2 \cdot 3 + 4 (- \log_{9} (7))$

Step 7

Multiply $2$ by $3$ .

$6 + 4 (- \log_{9} (7))$

Step 8

Multiply $- 1$ by $4$ .

$6 - 4 \log_{9} (7)$