Write as a Single Logarithm -5/2 log base 2 of 4-4 log base 2 of x+3/2 log base 2 of y

$- \frac{5}{2} \log_{2} (4) - 4 \log_{2} (x) + \frac{3}{2} \log_{2} (y)$

Logarithm base $2$ of $4$ is $2$ .

$- \frac{5}{2} \cdot 2 - 4 \log_{2} (x) + \frac{3}{2} \cdot \log_{2} (y)$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$\frac{- 5}{2} \cdot 2 - 4 \log_{2} (x) + \frac{3}{2} \cdot \log_{2} (y)$

Cancel the common factor.

$\frac{- 5}{2} \cdot 2 - 4 \log_{2} (x) + \frac{3}{2} \cdot \log_{2} (y)$

Rewrite the expression.

$- 5 - 4 \log_{2} (x) + \frac{3}{2} \cdot \log_{2} (y)$

Simplify $- 4 \log_{2} (x)$ by moving $4$ inside the logarithm.

$- 5 - \log_{2} (x^{4}) + \frac{3}{2} \cdot \log_{2} (y)$

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

$- 5 - \log_{2} (x^{4}) + \log_{2} (y^{\frac{3}{2}})$