Precalculus Examples

$\log (\frac{a^{2} \sqrt[3]{b}}{10})$

Step 1

Rewrite $\log (\frac{a^{2} \sqrt[3]{b}}{10})$ as $\log (a^{2} \sqrt[3]{b}) - \log (10)$ .

$\log (a^{2} \sqrt[3]{b}) - \log (10)$

Step 2

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

$\log (a^{2} b^{\frac{1}{3}}) - \log (10)$

Step 3

Logarithm base $10$ of $10$ is $1$ .

$\log (a^{2} b^{\frac{1}{3}}) - 1 \cdot 1$

Step 4

Multiply $- 1$ by $1$ .

$\log (a^{2} b^{\frac{1}{3}}) - 1$

Step 5

Rewrite $\log (a^{2} b^{\frac{1}{3}})$ as $\log (a^{2}) + \log (b^{\frac{1}{3}})$ .

$\log (a^{2}) + \log (b^{\frac{1}{3}}) - 1$

Step 6

Expand $\log (a^{2})$ by moving $2$ outside the logarithm.

$2 \log (a) + \log (b^{\frac{1}{3}}) - 1$

Step 7

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

$2 \log (a) + \frac{1}{3} \log (b) - 1$

Step 8

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

$2 \log (a) + \frac{\log (b)}{3} - 1$