Precalculus Examples

$\log (\frac{a^{2}}{b^{7 \sqrt{c}}})$

Step 1

Rewrite $\log (\frac{a^{2}}{b^{7 \sqrt{c}}})$ as $\log (a^{2}) - \log (b^{7 \sqrt{c}})$ .

$\log (a^{2}) - \log (b^{7 \sqrt{c}})$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{c}$ as $c^{\frac{1}{2}}$ .

$\log (a^{2}) - \log (b^{7 c^{\frac{1}{2}}})$

Step 3

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

$2 \log (a) - \log (b^{7 c^{\frac{1}{2}}})$

Step 4

Expand $\log (b^{7 c^{\frac{1}{2}}})$ by moving $7 c^{\frac{1}{2}}$ outside the logarithm.

$2 \log (a) - (7 c^{\frac{1}{2}} \log (b))$

Step 5

Multiply $7$ by $- 1$ .

$2 \log (a) - 7 (c^{\frac{1}{2}} \log (b))$

Step 6

Remove parentheses.

$2 \log (a) - 7 c^{\frac{1}{2}} \log (b)$