已知log2(x+y)=log2x+log2y,则xy的取值范围是多少?

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

已知log2(x+y)=log2x+log2y,则xy的取值范围是多少?
log2(x+y)=log2x+log2y
log2[x+y]=log2[xy]
x+y=xy
所以
x+y>0
x>0
y>0

xy≤(x+y)²/4
x+y=xy
xy≤(xy)²/4
(xy)²-4xy≥0
xy(xy-4)≥0
得 xy≥4