Question

If A raised to a power X is equal to B,B raised to the power y is equal to C and C Raised to the power Z is equal to A then prove that XYZ is equal to 1

Answer 1

A^x=B.........................(1)
B^y=C......................(2)
C^z=A.......................(3)

from (1)
A^x=B
(C^z)^x=B      [from (3)]
C^xz=B
(B^y)xz=B      [from  (2)]
B^xyz=B
now base are equal,then by comparing powers
xyyz=1   showed.