Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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