Precalculus Examples

$\log (\sqrt[4]{x^{2} + y^{2}})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{x^{2} + y^{2}}$ as ${(x^{2} + y^{2})}^{\frac{1}{4}}$ .

$\log ({(x^{2} + y^{2})}^{\frac{1}{4}})$

Step 2

Expand $\log ({(x^{2} + y^{2})}^{\frac{1}{4}})$ by moving $\frac{1}{4}$ outside the logarithm.

$\frac{1}{4} \log (x^{2} + y^{2})$

Step 3

Combine $\frac{1}{4}$ and $\log (x^{2} + y^{2})$ .

$\frac{\log (x^{2} + y^{2})}{4}$