exc4libur wrote:
Bunuel wrote:
If \(x\) is not equal to 0 and \(x^y=1\), then which of the following must be true?
I. \(x=1\)
II. \(x=1\) and \(y=0\)
III. \(x=1\) or \(y=0\)
A. \(I\) only
B. \(II\) only
C. \(III\) only
D. \(I\) and \(III\) only
E. \(None\)
Bunuel I understand that if x=-1 and y=2, then all conditions are false.
Would this be a valid case, since x and y can be anything integer/non-integer:
if x={any integer not 1}, and y={anything} so that \(x^y=1\)?
If I understood you correctly, you are asking whether \(x^y=1\) could be true if x is not equal to 1. Yes, x^0 = 1 (where x is not 0). For example, 4^0 = 1, 3.7^0 = 1, ...
If \(x^y=1\), is there a solution where x={anything except for 1} and y={non-integer}?