Answer
$$\log_2 (\frac{ (x-y)^{\frac{3}{2}}}{(x^2 + y^2)^2})$$
Work Step by Step
$Combine$ $into$ $a$ $single$ $logarithm:$
$\frac{3}{2}\log_2 (x-y)$ - $2\log_2 (x^2+y^2)$
Use the Third Law of Logarithms for both portions
$\frac{3}{2}\log_2 (x-y)$ = $\log_2 (x-y)^{\frac{3}{2}}$
$2\log_2 (x^2 + y^2)$ = $\log_2 (x^2 + y^2)^2$
$\log_2 (x-y)^{\frac{3}{2}}$ - $\log_2 (x^2 + y^2)^2$
Use the Second Law of Logarithms
$\log_2 (x-y)^{\frac{3}{2}}$ - $\log_2 (x^2 + y^2)^2$ = $\log_2 (\frac{ (x-y)^{\frac{3}{2}}}{(x^2 + y^2)^2})$
$$\log_2 (\frac{ (x-y)^{\frac{3}{2}}}{(x^2 + y^2)^2})$$