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

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

Simplify each term.

Simplify $3 \log_{2} (x)$ by moving $3$ inside the logarithm.

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

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

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

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

$\log_{2} (\frac{x^{3}}{\frac{3}{x + 4}})$

Multiply the numerator by the reciprocal of the denominator.

$\log_{2} (x^{3} \frac{x + 4}{3})$

Combine $x^{3}$ and $\frac{x + 4}{3}$ .

$\log_{2} (\frac{x^{3} (x + 4)}{3})$