If $x^{2} + y^{2} = 25 x y$ then show that $2 l o g (x + y) = 3 l o g 3 + l o g x + l o g y$ .

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Solution

Adding 2xy on both sides, We get :
$x^{2} + y^{2} + 2 x y = 27 x y$

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

Applying log on both sides

$l o g (x + y)^{2} = l o g (27 x y) = l o g 27 + l o g x + l o g y 2 l o g (x + y) = 3 l o g 3 + l o g x + l o g y$

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