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If x\geq y, y> 1, \: Then \: log_{x}\:\frac{x}{y}+log_{y}\:\frac{y}{x}   can never be

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As learnt in

Relation between AM, GM and HM of two positive numbers -

AM\geqslant GM\geqslant HM

- wherein

Inequality of the three given means.

 

log_{x}\frac{x}{y} + log_{y} \frac{y}{x}

= 1-log_{x}y+1-log_{y}x

= 2-(log_{x}y+log_{y}x)

now log_{y}x+log_{x}y> 2

AM\geq GM


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