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If (logx)/(b-c)=(logy)/(c-a)=(logz)/(a-b...

If `(logx)/(b-c)=(logy)/(c-a)=(logz)/(a-b)` , then which of the following is/are true?

A

`xyz=1`

B

`x^a y^b z^c=1`

C

`x^(b+c)y^(c+b)=1`

D

`x y z=x^a y^b z^c`

Text Solution

Verified by Experts

Let `logx/(b-c) = logy/(c-a) = logz/(a-b) = k`
`=>logx = kb-kc,logy = kc-ka,logz = ka-kb`
`=>logx+logy+logz = kb-kc+kc-ka+ ka-kb`
`=>log(xyz) = 0`
`=>log(xyz) = log1`
`=>xyz = 1`
So, option `(a)` is the correct option.
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