Can anyone please help me in doing the following question:

Given that x^2 + y^2 = 6xy, find an equivalent expression to 2 log(x+y).

Thanks any help will be greatly appreciated. :confused:

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- October 26th 2007, 12:41 AMhakuLogarithms Question
Can anyone please help me in doing the following question:

Given that x^2 + y^2 = 6xy, find an equivalent expression to 2 log(x+y).

Thanks any help will be greatly appreciated. :confused: - October 26th 2007, 12:51 AMticbol
*Given that x^2 + y^2 = 6xy, find an equivalent expression to 2 log(x+y).*

2log(x+y)

= log[(x+y)^2]

= log[x^2 +2xy +y^2] ------------(i)

x^2 +y^2 = 6xy

Add 2xy to both sides,

x^2 +2xy +y^2 = 8xy

(x +y)^2 = 8xy

So,

2log(x+y)

= log(8xy) --------------answer.

Or,

= log(8) +log(x) +log(y)

= log(2^3) +log(x) +log(y)

= 3log(2) +log(x) +log(y) -------------answer also. - October 26th 2007, 04:33 AMhaku
:) Thanks for the help!