若集合{x,xy,lg(xy)}={0,|x|,y},则log8(x2+y2)=_.

问题描述:

若集合{x,xy,lg(xy)}={0,|x|,y},则log8(x2+y2)=______.

∵集合{x,xy,lg(xy)}={0,|x|,y},由集合中元素的互异性可得 xy=1,且 y=x=-1,
log8(x2+y2)=log82=

lg2
3lg2
=
1
3

故答案为
1
3