If the set {x, XY, LG (XY)} = {0, | x | y}, then log8 (x2 + Y2)=______ .

If the set {x, XY, LG (XY)} = {0, | x | y}, then log8 (x2 + Y2)=______ .

∵ set {x, XY, LG (XY)} = {0, | x |, y}, from the mutual difference of elements in the set, we can get xy = 1, and y = x = - 1, so log8 (x2 + Y2) = log82 = lg23lg2 = 13, so the answer is 13