If the set {x, XY, LG (XY)} is equal to {0, absolute value of X, y}, then what is log8 (x + y)?

If the set {x, XY, LG (XY)} is equal to {0, absolute value of X, y}, then what is log8 (x + y)?

From the meaning of the question: X, y can not be 0, only log (XY) = 0
xy=1
So there are: x = |x|, xy = y or x = y, xy = |x|
X = y = 1 or x = y = - 1
So log8 (x ^ 2 + y ^ 2) = log8 (2) = 1 / 3