Question

If a raise to a power x =b, b raise to a power y = c and c raise to a power z = a prove that xyz=1

Answer 1

Answer:

Step-by-step explanation:

It is given that a raise to a power x =b that is $a^x=b$,

b raise to a power y=c that is  $b^y=c$ and

c raise to a power z=a that is  $c^z=a/tex]</p><p>Now, multiply the above equations we get</p><p>[tex]a^x{\times}b^y{\times}c^z=b{\times}c{\times}a$

⇒$a^xb^yc^z=abc$

Comparing the LHS and RHS, we have

$x=1$, $y=1$ and $z=1$

Thus, $xyz=(1)(1)(1)=1$

Hence proved.

Answer 2

Step-by-step explanation:

$Given \:b = a^{x}\: --(1)$

$c = b^{y}\:---(2)\\and\\a = c^{z}$

$\implies a = \left(b^{y}\right)^{z}\: [from \:(2)]$

$=\left(b^{yz}\right)$

$=\left(a^{x}\right)^{yz}\: [from \:(1)]$

$a^{1}=\left(a^{xyz}\right)$

$1 = xyz$

____________________

$By\: Exponential\:Law :\\</p><p>If \: x^{m}=x^{n} \implies m=n$

___________________

•••♪