Question

a power x is equal to b b power Y is equal to C and C power Z is equal to a prove that x y z is equal to 1

Answer 1

given
[tex] a^{x} = b [/tex]--(i)
$b^{y}=c$--(ii)
[tex] c^{z}=a [/tex]--(iii)
use(iii)in(i)
$c^{zx}=b$---(iv)
use(ii)in(iv)
[tex] b^{xyz} =b [/tex]
here bases are equal hence powers are also equal
hence xyz=1

Answer 2

Answer:

given

givena^{x} = bax=b --(i)

givena^{x} = bax=b --(i)b^{y}=cby=c --(ii)

givena^{x} = bax=b --(i)b^{y}=cby=c --(ii)c^{z}=acz=a --(iii)

givena^{x} = bax=b --(i)b^{y}=cby=c --(ii)c^{z}=acz=a --(iii)use(iii)in(i)

givena^{x} = bax=b --(i)b^{y}=cby=c --(ii)c^{z}=acz=a --(iii)use(iii)in(i)c^{zx}=bczx=b ---(iv)

givena^{x} = bax=b --(i)b^{y}=cby=c --(ii)c^{z}=acz=a --(iii)use(iii)in(i)c^{zx}=bczx=b ---(iv)use(ii)in(iv)

givena^{x} = bax=b --(i)b^{y}=cby=c --(ii)c^{z}=acz=a --(iii)use(iii)in(i)c^{zx}=bczx=b ---(iv)use(ii)in(iv)b^{xyz} =bbxyz=b

givena^{x} = bax=b --(i)b^{y}=cby=c --(ii)c^{z}=acz=a --(iii)use(iii)in(i)c^{zx}=bczx=b ---(iv)use(ii)in(iv)b^{xyz} =bbxyz=bhere bases are equal hence powers are also equal

givena^{x} = bax=b --(i)b^{y}=cby=c --(ii)c^{z}=acz=a --(iii)use(iii)in(i)c^{zx}=bczx=b ---(iv)use(ii)in(iv)b^{xyz} =bbxyz=bhere bases are equal hence powers are also equalhence xyz=1