Question

Why 1^x = 1^y doesn't implies x=y??

Answer 1

because the value of x and y may be different.
1 to the power x means 1 and 1 to the power Y means 1, so they are equal.
but the value of x and y may not be equal.

Answer 2

1^x ≠ 1^y

Because consider a case in which

1²=1³

both are equal to 1 but their powers are not equal in the same way 1^x ≠ 1^y.

Hope it helps.

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