Question

a power x =b power y= c power z and abc= 1 then 1/x+1/y+1/z=?​

Answer 1

${\bold{\sf{a^{x}=b^{y}=c^{z}=k}}}$

${\bold{\sf{x=log_{a}k}}}$ ; ${\bold{\sf{y=log_{b}k}}}$ ; ${\bold{\sf{z=log_{c}k}}}$

$\frac{1}{x} + \frac{1}{y} + \frac{1}{z} \\ = \frac{1}{ log_{a}k } + \frac{1}{ log_{b}k } + \frac{1}{ log_{c}k } \\ = log_{k}(a )+ log_{k}(b) + log_{k}(c) \\ = log_{k}(abc) = log_{k}(1) = 0$

Answer 2

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