已知log2(x+y)=log2x+log2y,则x+y的取值范围是?

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已知log2(x+y)=log2x+log2y,则x+y的取值范围是?已知log2(x+y)=log2x+log2y,则x+y的取值范围是?已知log2(x+y)=log2x+log2y,则x+y的取

已知log2(x+y)=log2x+log2y,则x+y的取值范围是?
已知log2(x+y)=log2x+log2y,则x+y的取值范围是?

已知log2(x+y)=log2x+log2y,则x+y的取值范围是?
∵log2(x+y)=log2x+log2y
∴log2(x+y)=log2(xy)
∴x+y=xy, x>0,y>0
根据均值定理
xy≤[(x+y)/2]²=(x+y)²/4
∴x+y=xy≤(x+y)²/4
∴x+y≥4
x+y的取值范围是【4,+∞)