Expand the Logarithmic Expression log of (6(5+x)^4)/(x^2)

$\log (\frac{6 {(5 + x)}^{4}}{x^{2}})$

Step 1

Rewrite $\log (\frac{6 {(5 + x)}^{4}}{x^{2}})$ as $\log (6 {(5 + x)}^{4}) - \log (x^{2})$ .

$\log (6 {(5 + x)}^{4}) - \log (x^{2})$

Step 2

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

$\log (6 {(5 + x)}^{4}) - (2 \log (x))$

Step 3

Multiply $2$ by $- 1$ .

$\log (6 {(5 + x)}^{4}) - 2 \log (x)$

Step 4

Rewrite $\log (6 {(5 + x)}^{4})$ as $\log (6) + \log ({(5 + x)}^{4})$ .

$\log (6) + \log ({(5 + x)}^{4}) - 2 \log (x)$

Step 5

Expand $\log ({(5 + x)}^{4})$ by moving $4$ outside the logarithm.

$\log (6) + 4 \log (5 + x) - 2 \log (x)$

Step 6

Simplify each term.

Rewrite $\log (6)$ as $\log (2 (3))$ .

$\log (2 (3)) + 4 \log (5 + x) - 2 \log (x)$

Rewrite $\log (2 (3))$ as $\log (2) + \log (3)$ .

$\log (2) + \log (3) + 4 \log (5 + x) - 2 \log (x)$