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Solving for exponents in proportionality

  1. Jul 27, 2009 #1
    In an experiment I am performing, I observed the following:

    Result is directly proportional to A
    Result is inversely proportional to B

    So, I assume two constants, alpha and beta such that:

    Result = (A^alpha)/(B^beta)

    Now, if I know I want to solve for alpha and beta but is this the right approach to take to get the value of Result for any given A and B?

    (Actually, I could have assumed Result = k. (A/B) but I am not sure that my result follows such a simple proportionality which is why I assumed alpha and beta). Any input on this is appreciated. Thanks
     
  2. jcsd
  3. Jul 27, 2009 #2

    CRGreathouse

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    You also need a constant out front, for a total of 3 constants to be determined.
     
  4. Jul 27, 2009 #3
    So that means, I should in fact be looking at Result = k. (A^alpha) * (B^beta)? Could you provide me some insight on how to go about solving this equation? I am new to these things so even a direction would be helpful...

    I was actually thinking of determining alpha, beta and k on a trial and error basis experimentally but that would take me ages with the experiment I am running...
     
  5. Jul 27, 2009 #4

    CRGreathouse

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    Take logarithms, then it's just a high school algebra exercise to regress three points to it. If you have more data you can do a standard least-squares fit.
     
  6. Jul 27, 2009 #5
    Understood... Thanks so much for the help :)
     
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