Write as a Single Logarithm 3 log of x+4 log of x-2

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

Simplify each term.

Simplify $3 \log (x)$ by moving $3$ inside the logarithm.

$\log (x^{3}) + 4 \log (x - 2)$

Simplify $4 \log (x - 2)$ by moving $4$ inside the logarithm.

$\log (x^{3}) + \log ({(x - 2)}^{4})$

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log (x^{3} {(x - 2)}^{4})$