Algebra Examples

$\log_{b} (x^{4} \sqrt[3]{y})$

Step 1

Rewrite $\log_{b} (x^{4} \sqrt[3]{y})$ as $\log_{b} (x^{4}) + \log_{b} (\sqrt[3]{y})$ .

$\log_{b} (x^{4}) + \log_{b} (\sqrt[3]{y})$

Step 2

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

$\log_{b} (x^{4}) + \log_{b} (y^{\frac{1}{3}})$

Step 3

Expand $\log_{b} (x^{4})$ by moving $4$ outside the logarithm.

$4 \log_{b} (x) + \log_{b} (y^{\frac{1}{3}})$

Step 4

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

$4 \log_{b} (x) + \frac{1}{3} \log_{b} (y)$

Step 5

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

$4 \log_{b} (x) + \frac{\log_{b} (y)}{3}$