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Dividing Functions

  1. Apr 1, 2007 #1
    How would one go about dividing two exponential functions.
    Basically I have f(x)=k*g(x)
    So to solve for k, k=f(x)/g(x)
    How would one accomplish this when the functions are both within the format:

  2. jcsd
  3. Apr 1, 2007 #2
    There's usually no nice simplification when there's a sum in the denominator.
  4. Apr 1, 2007 #3
    There is a way to simplify, but it's not necessarily what you are looking for. You might or might not end up with an invariant remainder. Here:

    [tex]\frac{Ae^{Cx} + B}{Oe^{Px} + Q}[/tex]

    For example, let's say A = 1 and P = 1

    [tex]\frac{Ae^{x} + B}{Oe^{x} + Q}[/tex]

    Make the substitution e^x = y and get

    [tex]\frac{Ay + B}{Oy + Q}[/tex]

    Now we can write

    [tex]\frac{A/O(Oy + Q - Q) + B}{Oy + Q}[/tex]

    [tex]\frac{A/O(Oy + Q ) - QA/O + B}{Oy + Q}[/tex]

    [tex]A/O + \frac{B - QA/O}{Oy + Q}[/tex]

    B - QA/O is the remainder here.
    Last edited: Apr 1, 2007
  5. Apr 3, 2007 #4
    Hmm I will try your method Werg but like you say I am not sure it is what I am looking for.
    I am also trying to make both individual functions into linear expressions by taking the natural log of both sides however I run into natrual log rules which keep this from succeeding. Any ideas in the department?
    Another note, I would like to clarify that I should have represented the functions as something like:
    they are both describing different attributes of a system. What I am trying to accomplish is finding a relationship between n and v. Still working towards a solution so any help greatly appreciated.

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