Question

If X²+y² =25xy prove that 2 log (x+y) = log x +log x + log y +3log³

Answer 1

$Given \: x^{2} + y^{2} = 25xy$

$\implies x^{2} + y^{2} + 2xy = 25xy + 2xy$

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

$\implies (x+ y)^{2} = 3^{3}xy$

$\implies log (x+y)^{2} = log ( 3^{3}xy )$

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

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*/ By Logarithmic laws /*

1. log aⁿ = n log a

2. log mn = log m + log n

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$\implies 2 log (x+y) =3 log 3+ log x + log y$

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