Precalculus Examples

$\log_{2} (11 \sqrt[3]{3})$

Step 1

Rewrite $\log_{2} (11 \sqrt[3]{3})$ as $\log_{2} (11) + \log_{2} (\sqrt[3]{3})$ .

$\log_{2} (11) + \log_{2} (\sqrt[3]{3})$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{3}$ as $3^{\frac{1}{3}}$ .

$\log_{2} (11) + \log_{2} (3^{\frac{1}{3}})$

Step 3

Expand $\log_{2} (3^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$\log_{2} (11) + \frac{1}{3} \log_{2} (3)$

Step 4

Combine $\frac{1}{3}$ and $\log_{2} (3)$ .

$\log_{2} (11) + \frac{\log_{2} (3)}{3}$