Algebra Examples

$\log (\frac{x \sqrt[3]{z^{4}}}{y})$

Step 1

Rewrite $\log (\frac{x \sqrt[3]{z^{4}}}{y})$ as $\log (x \sqrt[3]{z^{4}}) - \log (y)$ .

$\log (x \sqrt[3]{z^{4}}) - \log (y)$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{z^{4}}$ as $z^{\frac{4}{3}}$ .

$\log (x z^{\frac{4}{3}}) - \log (y)$

Step 3

Rewrite $\log (x z^{\frac{4}{3}})$ as $\log (x) + \log (z^{\frac{4}{3}})$ .

$\log (x) + \log (z^{\frac{4}{3}}) - \log (y)$

Step 4

Expand $\log (z^{\frac{4}{3}})$ by moving $\frac{4}{3}$ outside the logarithm.

$\log (x) + \frac{4}{3} \log (z) - \log (y)$

Step 5

Combine $\frac{4}{3}$ and $\log (z)$ .

$\log (x) + \frac{4 \log (z)}{3} - \log (y)$