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Solve a system equation

  1. Dec 18, 2012 #1
    Hi everybody,
    Please I want to Solve the system:


    x,y real number!

    Thank you !
  2. jcsd
  3. Dec 18, 2012 #2


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    I think clever guessing (and showing that there are not other solutions) is the quickest method. You can solve one of those equations for a single variable and put this into the other equation, but I don't think you cannot simply find solutions like that.
  4. Dec 18, 2012 #3


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    It looks like 3,3 is the only solution.
  5. Dec 19, 2012 #4


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    There is another solution near y=20.8216, x=13.1370.
  6. Dec 19, 2012 #5
    Please I want the steps to find it, because I'm stumbled in the last steps as follow:

    x*Ln(3)-y*Ln(2) - 3*Ln(y)-x*Ln(2) = 0
    x*Ln(3)+x*Ln(2) = y*Ln(2)+3*Ln(y) {each one equals Ln(19)}
    x*Ln(3)+x*Ln(2) = y*Ln(2)+3*Ln(y) = Ln(19)
    x*Ln(6) = y*Ln(2)+3*Ln(y) = Ln(19)

    x = ln(19)/ln(6)

    Here I'm stumbled.

    Thank you for your response.
  7. Dec 19, 2012 #6


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    There is no useful way to simplify ln(19)/ln(6). It is just some number - and it is wrong.

    The first step does not work. ln(a-b) is not the same as ln(a) - ln(b).
    The third step looks wrong, too (where you say "{each one equals Ln(19)}").
  8. Dec 19, 2012 #7


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    The first equation below is wrong, so everything below it is also invalid.

    You apparently took the natural log of both sides, like so:
    ln(3x - 2y) = ln(19)

    Then you "distributed" the ln operation like this:
    ln(3x) - ln(2y) = ln(19)
    This is the step that is incorrect. There is no property of logs in which ln(A + B) = ln(A) + ln(B).

  9. Dec 19, 2012 #8
    Thank you all.
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