Precalculus Examples

$\log (\sqrt[11]{100})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[11]{100}$ as $100^{\frac{1}{11}}$ .

$\log (100^{\frac{1}{11}})$

Step 2

Expand $\log (100^{\frac{1}{11}})$ by moving $\frac{1}{11}$ outside the logarithm.

$\frac{1}{11} \log (100)$

Step 3

Logarithm base $10$ of $100$ is $2$ .

$\frac{1}{11} \cdot 2$

Step 4

Combine $\frac{1}{11}$ and $2$ .

$\frac{2}{11}$