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Help!! P2 logarithm question, too tough for me watch

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    Hi, This one is a real problem for me,

    If xy=64 and log(basex)y + log(basey)x = 5/2

    find x and y

    ---------------------------------------

    After changing the base I get

    (lgy/lgx) + (lgx/lgy) = 5/2

    After this I keep getting it wrong? any ideas?

    thanks
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    change to one base (x or y or e or 10)
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    (Original post by kikzen)
    change to one base (x or y or e or 10)
    already done that!!! lgx equals log (base 10) x

    anyways here is the answer just go it

    (lgy/lgx) + (lgx/lgy) = 5/2

    (2)(lgy)(lgy)+(2)(lgx)(lgx)= 5(lgx)(lgy)

    let lgy=t
    let lgx=v

    so, 2t^2 - 5tv + 2v^2 = 0

    (2t - v)(t-2v)

    (1) v=2t and (2) t=2v



    from (1)

    lgx = 2lgy

    but xy = 64

    lgx + lgy = lg64

    therefore 2lgy + lgy = lg64

    3lgy = 3lg4

    so y=4

    xy = 64

    so x=16



    from (2)

    lgy = 2lgx

    but xy = 64

    lgx + lgy = lg64

    therefore 2lgx + lgx = lg64

    3lgx = 3lg4

    so x=4

    xy = 64

    so x=16



    so the answer is (16,4) or (4,16)


    I think it's because (lgx)(lgx) can only be solved by letting it equal something else like t, then factorising.
 
 
 
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