Precalculus Examples

$\log (\sqrt{x^{9} - y})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x^{9} - y}$ as ${(x^{9} - y)}^{\frac{1}{2}}$ .

$\log ({(x^{9} - y)}^{\frac{1}{2}})$

Step 2

Expand $\log ({(x^{9} - y)}^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\frac{1}{2} \log (x^{9} - y)$

Step 3

Combine $\frac{1}{2}$ and $\log (x^{9} - y)$ .

$\frac{\log (x^{9} - y)}{2}$