Calculus Examples

$\log (\frac{x (x + 2)}{{(x + 6)}^{5}})$

Step 1

Rewrite $\log (\frac{x (x + 2)}{{(x + 6)}^{5}})$ as $\log (x (x + 2)) - \log ({(x + 6)}^{5})$ .

$\log (x (x + 2)) - \log ({(x + 6)}^{5})$

Step 2

Expand $\log ({(x + 6)}^{5})$ by moving $5$ outside the logarithm.

$\log (x (x + 2)) - (5 \log (x + 6))$

Step 3

Multiply $5$ by $- 1$ .

$\log (x (x + 2)) - 5 \log (x + 6)$

Step 4

Rewrite $\log (x (x + 2))$ as $\log (x) + \log (x + 2)$ .

$\log (x) + \log (x + 2) - 5 \log (x + 6)$