Question

If a^x = b, b^y = c and c^z = a, prove that : xyz = 1.

Answer 1

We are given that
a^x = b, b^y = c and c^z = a
Consider the equation
a^x = b
⇒ a^xyz = b^yz      [ raising to the power yz on both sides ] 
⇒  a^xyz = (b^y)^z
⇒ a^xyz = c^z         [ ∵ b^y = c ]
⇒  a^xyz = c^z
⇒  a^xyz = a         [ ∵ c^z = a ]
⇒  a^xyz = a¹
⇒  xyz = 1