Simplify/Condense 4 log of x-6 log of x+2

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

Step 1

Simplify each term.

Simplify $4 \log (x)$ by moving $4$ inside the logarithm.

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

Simplify $- 6 \log (x + 2)$ by moving $6$ inside the logarithm.

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

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

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