Expand the Logarithmic Expression log of (4(8+x)^2)/(x^5)

$\log (\frac{4 {(8 + x)}^{2}}{x^{5}})$

Rewrite $\log (\frac{4 {(8 + x)}^{2}}{x^{5}})$ as $\log (4 {(8 + x)}^{2}) - \log (x^{5})$ .

$\log (4 {(8 + x)}^{2}) - \log (x^{5})$

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

$\log (4 {(8 + x)}^{2}) - (5 \log (x))$

Multiply $5$ by $- 1$ .

$\log (4 {(8 + x)}^{2}) - 5 \log (x)$

Rewrite $\log (4 {(8 + x)}^{2})$ as $\log (4) + \log ({(8 + x)}^{2})$ .

$\log (4) + \log ({(8 + x)}^{2}) - 5 \log (x)$

Expand $\log ({(8 + x)}^{2})$ by moving $2$ outside the logarithm.

$\log (4) + 2 \log (8 + x) - 5 \log (x)$

Simplify each term.

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

$\log (2^{2}) + 2 \log (8 + x) - 5 \log (x)$

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

$2 \log (2) + 2 \log (8 + x) - 5 \log (x)$