Question

If $a^x=b,b^y=c,c^z=a$ then show that $xyz=1$.

Answer 1

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

Now putting the value of $c$ from (2) in (3) we get,

$b^{yz}=a$

Now using the value of $b$ from (1) in the above equation we get,

$a^{xyz}=a$

or, $xyz=1$.