Precalculus Examples

$6 \log_{9} (\sqrt[3]{y})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{y}$ as $y^{\frac{1}{3}}$ .

$6 \log_{9} (y^{\frac{1}{3}})$

Step 2

Expand $\log_{9} (y^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$6 (\frac{1}{3} \log_{9} (y))$

Step 3

Combine $\frac{1}{3}$ and $\log_{9} (y)$ .

$6 \frac{\log_{9} (y)}{3}$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Factor $3$ out of $6$ .

$3 (2) \frac{\log_{9} (y)}{3}$

Step 4.2

Cancel the common factor.

$3 \cdot 2 \frac{\log_{9} (y)}{3}$

Step 4.3

Rewrite the expression.

$2 \log_{9} (y)$