Problem: If ∣x−logy∣=x+logy where x and logy are real, then
Answer Choices:
A. x=0
B. y=1
C. x=0 and y=1
D. x(y−1)=0
E. None of these
Solution:
if (x−logy) is nonnegative, then the given equation requires that x−logy=x+logy to that −logy=logy=0 and y=1. On the other hand, if (x−logy) is negative −(x−logy)=x+logy so that 2x=0. We can write x(y−1)=0 to any that x=0 or y=1 or both.