2014/045) Solve for x: (ab)^2 =(bc)^ 4 =(ca)^ x =abc

we have ab = (abc)^(1/2)
bc = (abc)^(1/4)
ca = (abc)^(1/x)
multiply and get
(abc)^2 = (abc)^(1/2 + 1/4 + 1/x)

hence 1/2 + 1/4 + 1/x = 2 or x = 4/5