If $\frac{1}{2} l o g (x + y) = log 2 x + log 3 y$ , find the relationship between x and y.

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Solution

$\frac{1}{2} log (x + y) = log 2 x + log 3 y$
$log (x + y)^{\frac{1}{2}} = log (2 x . 3 y)$
$\Rightarrow (x + y)^{\frac{1}{2}} = 6 x y$
$\Rightarrow (x + y) = 36 x^{2} y^{2}$

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