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

  • Option 1)

    -1

  • Option 2)

    -0.5

  • Option 3)

    0

  • Option 4)

    1

 

Answers (1)

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


Option 1)

-1

This solution is incorrect

Option 2)

-0.5

This solution is incorrect

Option 3)

0

This solution is incorrect

Option 4)

1

This solution is correct

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