Precalculus Examples

$\log_{8} (x y^{5 \sqrt[3]{z}})$

Step 1

Rewrite $\log_{8} (x y^{5 \sqrt[3]{z}})$ as $\log_{8} (x) + \log_{8} (y^{5 \sqrt[3]{z}})$ .

$\log_{8} (x) + \log_{8} (y^{5 \sqrt[3]{z}})$

Step 2

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

$\log_{8} (x) + \log_{8} (y^{5 z^{\frac{1}{3}}})$

Step 3

Expand $\log_{8} (y^{5 z^{\frac{1}{3}}})$ by moving $5 z^{\frac{1}{3}}$ outside the logarithm.

$\log_{8} (x) + 5 z^{\frac{1}{3}} \log_{8} (y)$