Precalculus Examples

$\log_{6} (\frac{x (x + 6)}{{(x + 3)}^{6}})$

Step 1

Rewrite $\log_{6} (\frac{x (x + 6)}{{(x + 3)}^{6}})$ as $\log_{6} (x (x + 6)) - \log_{6} ({(x + 3)}^{6})$ .

$\log_{6} (x (x + 6)) - \log_{6} ({(x + 3)}^{6})$

Step 2

Expand $\log_{6} ({(x + 3)}^{6})$ by moving $6$ outside the logarithm.

$\log_{6} (x (x + 6)) - (6 \log_{6} (x + 3))$

Step 3

Multiply $6$ by $- 1$ .

$\log_{6} (x (x + 6)) - 6 \log_{6} (x + 3)$

Step 4

Rewrite $\log_{6} (x (x + 6))$ as $\log_{6} (x) + \log_{6} (x + 6)$ .

$\log_{6} (x) + \log_{6} (x + 6) - 6 \log_{6} (x + 3)$