1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook