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Math Help - Logarithms Question

  1. #1
    Junior Member
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    Oct 2007
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    Question Logarithms 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.
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  2. #2
    MHF Contributor
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    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.
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  3. #3
    Junior Member
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    Thanks for the help!
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