Write as a Single Logarithm 4 log base 1/2 of w+(2 log base 1/2 of u-3 log base 1/2 of v)

$4 \log_{\frac{1}{2}} (w) + (2 \log_{\frac{1}{2}} (u) - 3 \log_{\frac{1}{2}} (v))$

Remove parentheses.

$4 \log_{\frac{1}{2}} (w) + 2 \log_{\frac{1}{2}} (u) - 3 \log_{\frac{1}{2}} (v)$

Simplify each term.

Simplify $4 \log_{\frac{1}{2}} (w)$ by moving $4$ inside the logarithm.

$\log_{\frac{1}{2}} (w^{4}) + 2 \log_{\frac{1}{2}} (u) - 3 \log_{\frac{1}{2}} (v)$

Simplify $2 \log_{\frac{1}{2}} (u)$ by moving $2$ inside the logarithm.

$\log_{\frac{1}{2}} (w^{4}) + \log_{\frac{1}{2}} (u^{2}) - 3 \log_{\frac{1}{2}} (v)$

Simplify $- 3 \log_{\frac{1}{2}} (v)$ by moving $3$ inside the logarithm.

$\log_{\frac{1}{2}} (w^{4}) + \log_{\frac{1}{2}} (u^{2}) - \log_{\frac{1}{2}} (v^{3})$

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

$\log_{\frac{1}{2}} (w^{4} u^{2}) - \log_{\frac{1}{2}} (v^{3})$

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

$\log_{\frac{1}{2}} (\frac{w^{4} u^{2}}{v^{3}})$