Expand the Logarithmic Expression log of (2(7+x)^4)/(x^5)

$\log (\frac{2 {(7 + x)}^{4}}{x^{5}})$

Step 1

Rewrite $\log (\frac{2 {(7 + x)}^{4}}{x^{5}})$ as $\log (2 {(7 + x)}^{4}) - \log (x^{5})$ .

$\log (2 {(7 + x)}^{4}) - \log (x^{5})$

Step 2

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

$\log (2 {(7 + x)}^{4}) - (5 \log (x))$

Step 3

Multiply $5$ by $- 1$ .

$\log (2 {(7 + x)}^{4}) - 5 \log (x)$

Step 4

Rewrite $\log (2 {(7 + x)}^{4})$ as $\log (2) + \log ({(7 + x)}^{4})$ .

$\log (2) + \log ({(7 + x)}^{4}) - 5 \log (x)$

Step 5

Expand $\log ({(7 + x)}^{4})$ by moving $4$ outside the logarithm.

$\log (2) + 4 \log (7 + x) - 5 \log (x)$