Question

if log (x square + Y square ) = log 2 + log x + log Y ,then show that x=y​

Answer 1

$Given \: log (x^{2} + y^{2} ) = log 2 + log x + log y$

$\implies log (x^{2} + y^{2} ) = log 2 x y$

$\boxed{\pink{ \because log m + log n = log ( mn ) }}$

$\implies x^{2} + y^{2} = 2xy$

$\implies x^{2} + y^{2} - 2xy = 0$

$\implies (x-y)^{2} = 0$

$\implies x - y = 0$

$\implies \blue { x = y }$

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