若实数x，y满足条件log2x+log2（x-y）=1+2log2y，则log2xy=．

Question

若实数x，y满足条件log₂x+log₂（x-y）=1+2log₂y，则log2(x)/(y)=______．

Answer 1

由log₂x+log₂（x-y）=1+2log₂y，
得x＞0，y＞0，且log2x(x-y)=log22y2
即x²-xy=2y²，
∴((x)/(y))2-(x)/(y)-2=0
解得(x)/(y)=-1（舍）或(x)/(y)=2．
则log2(x)/(y)=1．
故答案为1．