Which is true?

$x = y^a$ => $\boxed{log x = a (log y)}$ .. (1)

$y = z^b$ => $\boxed{log y = b (log z)}$ .. (2)

$z = x^c$ => $\boxed{log z = c (log x)}$ .. (3)

$log x = a (log y) = ab (log z) = abc (log x)$ [substitute (2) to (1) and substitute (3) to the resulting equation]

$\boxed{abc = 1}$

$\large{y = x^{\frac{1}{a}} \Rightarrow\ x^{\frac{1}{a}} = z^b}$ $\large{\Rightarrow\ x = z^{ab} \Rightarrow\ x^c = z^{abc} = z}$ $\Huge{\therefore\ abc = 1}$

Multiply all three equations xyz = (xyz)^(abc) Therefore abc =1

y = z^b
y = x^(bc)
y = y^(abc)
therefore abc = 1(Ans.)