设正数xy满足log2(x+y+3)=log2x+log2y,求xy取值范围

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设正数xy满足log2(x+y+3)=log2x+log2y,求xy取值范围

设正数xy满足log2(x+y+3)=log2x+log2y,求xy取值范围
设正数xy满足log2(x+y+3)=log2x+log2y,求xy取值范围

设正数xy满足log2(x+y+3)=log2x+log2y,求xy取值范围
由已知
log2(x+y+3)=log2(xy)
可得xy=x+y+3≥2√xy+3
得(√xy-3)(√xy+1)≥0
得√xy≥3
得xy≥9

∵loga(b)+loga(c)=loga(bc)
∴log2(x+y+3)=log2(x)+log2(y)=log2(xy)
∴x+y+3=xy
I5