Question

If x^2 + y^2 =25xy,then prove that 2 log [x+y]=3log^3+logx+log y

Answer 1

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Let,

$( {x + y}^{2} ) = {x}^{2} + {y}^{2} + 2xy$


$( {x + y}^{2} ) = 25xy + 2xy$


$( {x + y)}^{2} = 27xy$


Now apply the log on both side...


$log( {x + y}^{2} ) = log(27xy)$

$2 log(x + y) = log27 + logx + log \: y$

$2log(x + y) = {log}^{ {3}^{3} } + logx + log(y)$

$2log(x + y) = 3 {log}^{3} + logx + logy$

Hence proved...


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Answer 2

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