How do you prove that xyz equals 1 if x equals logy z and y equals logz x and z equals logx y?

Answer 1

If xyz=1, then it is very likely that x=1, y=1, and z=1. So plug these in. 1=logbase1of1, 1=logbase1of1, 1=logbase1of1. You end up with 1=1, 1=1, and 1=1. That's your proof.