Question

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

Answer 1

Answer:

Step-by-step 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