Precalculus Examples

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

Step 1

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

$\frac{1}{3} \log (x y)$

Step 2

Rewrite $\log (x y)$ as $\log (x) + \log (y)$ .

$\frac{1}{3} (\log (x) + \log (y))$

Step 3

Apply the distributive property.

$\frac{1}{3} \log (x) + \frac{1}{3} \log (y)$

Step 4

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

$\frac{\log (x)}{3} + \frac{1}{3} \log (y)$

Step 5

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

$\frac{\log (x)}{3} + \frac{\log (y)}{3}$