Question

if a x =b , b y =c , c z =a then prove that xyz=1

Answer 1

x=b/a
y=c/b
z= a/c
Now
LHS
xyz
=b/a x c/b x a/c
=1
=RHS

Answer 2

Given,
aˣ = b,$b^{y} = c , c^{z} = a$
$c^{z} = a$, c is what it is $b^{y}$
so, $b^{yz} = a$
Now b is what is $a^{x}$
$[a^{x}]^{yz} = a$
$a^{xyz} = a$
$a^{xyz} = a^{1}$
Therefore,
xyz = 1

[Hence Proved]