2. If $\log _{2}(x+y)=\log _{2} x+\log _{2} y$, then the range of $x+y$ is
A. $(0,1]$
B. $[2,+\infty)$
C. $(0,4]$
D. $[4,+\infty)$
2. D $x+y=x y$, and $x>0, y>0$, by the AM-GM inequality $x+y=x y \geqslant 2 \sqrt{x y}, \sqrt{x y} \geqslant 2, x y \geqslant 4$, i.e., $x+$ $y \geqslant 4$, and equality holds if and only if $x=y=2$.