Linear Algebra Examples

$\log_{6} (\frac{a b^{4}}{\sqrt[3]{c^{2}}})$

Step 1

Rewrite $\log_{6} (\frac{a b^{4}}{\sqrt[3]{c^{2}}})$ as $\log_{6} (a b^{4}) - \log_{6} (\sqrt[3]{c^{2}})$ .

$\log_{6} (a b^{4}) - \log_{6} (\sqrt[3]{c^{2}})$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{c^{2}}$ as $c^{\frac{2}{3}}$ .

$\log_{6} (a b^{4}) - \log_{6} (c^{\frac{2}{3}})$

Step 3

Expand $\log_{6} (c^{\frac{2}{3}})$ by moving $\frac{2}{3}$ outside the logarithm.

$\log_{6} (a b^{4}) - (\frac{2}{3} \log_{6} (c))$

Step 4

Combine $\frac{2}{3}$ and $\log_{6} (c)$ .

$\log_{6} (a b^{4}) - \frac{2 \log_{6} (c)}{3}$

Step 5

Rewrite $\log_{6} (a b^{4})$ as $\log_{6} (a) + \log_{6} (b^{4})$ .

$\log_{6} (a) + \log_{6} (b^{4}) - \frac{2 \log_{6} (c)}{3}$

Step 6

Expand $\log_{6} (b^{4})$ by moving $4$ outside the logarithm.

$\log_{6} (a) + 4 \log_{6} (b) - \frac{2 \log_{6} (c)}{3}$