Question

x = 3^a, y = 9^b, z = 27^c and x^bc, y^ca z^ab = 1, then abc is equal to​

Answer 1

Given info : x = 3^a, y = 9^b, z = 27^c and x^bc = y^ca = z^ab = 1

To find : the value of abc

solution : x = 3^a , y ^ 9^b, z = 27^c

x^bc = (3^a)^bc = 1

⇒3^(abc) = 1 ......(1)

y^ca = (9^b)^ca = 1

⇒9^(abc) = 1 .......(2)

z^ab = (27^c)^ab = 1

⇒27^(abc) = 1 ......(3)

from equations (1) , (2) and (3),

3^(abc) = 9^(abc) = 27^(abc) = 1 , it is possible only when abc = 0

i.e., 3⁰ = 9⁰ = 27⁰ = 1

Therefore the value of abc = 0