Question

If $x^a=y$, $y^b=z$ and $z^c=x$, then prove that $abc=1$

Answer 1

Let, $x^a=y$......(1) and $y^b=z$.....(2) and $z^c=x$......(3).

Now, using (1) in (2) we get,

$x^{ab}=z$......(4).

Now, using (4) in (3) we get,

$x^{abc}=x$

or, $x^{abc}=x^1$

or, $abc=1$.