Precalculus Examples

$\log_{3} ({(\frac{7 x}{y})}^{\frac{1}{3}})$

Step 1

Expand $\log_{3} ({(\frac{7 x}{y})}^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$\frac{1}{3} \log_{3} (\frac{7 x}{y})$

Step 2

Rewrite $\log_{3} (\frac{7 x}{y})$ as $\log_{3} (7 x) - \log_{3} (y)$ .

$\frac{1}{3} (\log_{3} (7 x) - \log_{3} (y))$

Step 3

Rewrite $\log_{3} (7 x)$ as $\log_{3} (7) + \log_{3} (x)$ .

$\frac{1}{3} (\log_{3} (7) + \log_{3} (x) - \log_{3} (y))$

Step 4

Apply the distributive property.

$\frac{1}{3} \log_{3} (7) + \frac{1}{3} \log_{3} (x) + \frac{1}{3} (- \log_{3} (y))$

Step 5

Simplify.

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Step 5.1

Combine $\frac{1}{3}$ and $\log_{3} (7)$ .

$\frac{\log_{3} (7)}{3} + \frac{1}{3} \log_{3} (x) + \frac{1}{3} (- \log_{3} (y))$

Step 5.2

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

$\frac{\log_{3} (7)}{3} + \frac{\log_{3} (x)}{3} + \frac{1}{3} (- \log_{3} (y))$

Step 5.3

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

$\frac{\log_{3} (7)}{3} + \frac{\log_{3} (x)}{3} - \frac{\log_{3} (y)}{3}$