Question

If a = b^c b=c^a and c =a^b prove abc =1​

Answer 1

Explanation:

`a = b^(c)` ------------(I)

Plug in b =
`c^(a)`

(I) --->
`a = (c^(a))^(c)= \ c^(a*c) = \ c^(ac)` -----------(II)

Plug in c =
`a^(b)`

(II) ----->

`a = (a^(b))^(ac) \\\\a = a^(ac*b)\\\\a = a^(abc)`

Both sides base are same. So, compare the powers

1 = abc

abc = 1

Hence proved