If $a=b^x, b=c^y$ and $c=a^z$ then find the value of xyz.
(A) 0
(B) 1(C) 2
(D) 5
(E) None of these

Given:

$a=b^x, b=c^y$ and $c=a^z$.

To do:

We have to find the value of $xyx$.
Solution:

$a=b^x$

$a=(c^y)^x$     (Since $b=c^y$)

$a=c^{xy}$       (Since $(a^m)^n=a^{mn}$)
$a=(a^z)^{xy}$   (Since $c=a^z$)

$a=a^{xyz}$

Equating powers on both sides, we get,

$xyz=1$

The value of $xyz$ is $1$.

Tutorialspoint

e

Updated on: 10-Oct-2022

55 Views

Kickstart Your Career

Get certified by completing the course

Get Started