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If (log x)/(b-c) = (log y)/(c-a) = (log ...

If `(log x)/(b-c) = (log y)/(c-a) = (log z)/(a-b)`, then which of the following is/are true?

Text Solution

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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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