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Changing the subject of this equation

  1. Nov 2, 2012 #1
    I am having difficulty making x the subject of the following formula.

    y = [a.e^(b.x)] + [c.e^(d.x)]

    I thought the first step would be to take the natural log of both sides of the equation:

    ln(y) = ln(a)+b.x+ln(c)+d.x

    But this does not work, even though the following is correct:

    y = a.e^x
    ln(y) = ln(a) + x

    I am a little stuck as to what to try next!

  2. jcsd
  3. Nov 2, 2012 #2


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    Homework Helper

    The problem is, you can't make x the subject! At least it's not expressible in terms of finitely many elementary functions we commonly use, such as logs, powers, trig etc.
  4. Nov 2, 2012 #3
    I had a feeling this was going to be the outcome... damnit!!
  5. Nov 2, 2012 #4


    Staff: Mentor

    The reason this doesn't work is that ln(A + B) ≠ ln(A) + ln(B). You cannot take the log of a sum and get the sum of the logs.
  6. Nov 5, 2012 #5
    I see, thankyou. So there is no way at all to make x the subject in this case?
  7. Nov 5, 2012 #6


    User Avatar
    Homework Helper

    There is, but it'd be in terms of an infinite sum, which is even less useful than just finding a numerical approximation to x.
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