Solving for exponents in proportionality

  • #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
 

Answers and Replies

  • #2
CRGreathouse
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You also need a constant out front, for a total of 3 constants to be determined.
 
  • #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...
 
  • #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.
 
  • #5
Understood... Thanks so much for the help :)
 

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