Precalculus Examples

$\log_{a} (\sqrt[9]{x y})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[9]{x y}$ as ${(x y)}^{\frac{1}{9}}$ .

$\log_{a} ({(x y)}^{\frac{1}{9}})$

Step 2

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

$\frac{1}{9} \log_{a} (x y)$

Step 3

Rewrite $\log_{a} (x y)$ as $\log_{a} (x) + \log_{a} (y)$ .

$\frac{1}{9} (\log_{a} (x) + \log_{a} (y))$

Step 4

Apply the distributive property.

$\frac{1}{9} \log_{a} (x) + \frac{1}{9} \log_{a} (y)$

Step 5

Combine $\frac{1}{9}$ and $\log_{a} (x)$ .

$\frac{\log_{a} (x)}{9} + \frac{1}{9} \log_{a} (y)$

Step 6

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

$\frac{\log_{a} (x)}{9} + \frac{\log_{a} (y)}{9}$