Solving for exponents in proportionality

In summary, the conversation discusses an experiment being performed where it is observed that the result is directly proportional to A and inversely proportional to B. The individual is considering using two constants, alpha and beta, to solve for the result. However, they are unsure if this is the correct approach and are seeking advice on how to solve the equation. It is suggested to also include a constant out front, for a total of three constants to be determined. The individual is considering using trial and error or logarithms to solve the equation.
  • #1
EliteLegend
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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
 
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  • #2
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
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 :)
 

1. What is an exponent?

An exponent is a number that represents how many times a base number is multiplied by itself. It is written as a superscript to the right of the base number.

2. How do I solve for an exponent in proportionality?

To solve for an exponent in proportionality, you can use the property of logarithms which states that logbx = y if and only if by = x.

3. What is the inverse relationship between exponents and logarithms?

The inverse relationship between exponents and logarithms is that they "undo" each other. In other words, if you take the logarithm of a number and then raise it to the power of the same base, you will get back the original number.

4. How do I solve for a variable with an exponent in a proportionality equation?

To solve for a variable with an exponent in a proportionality equation, you need to isolate the variable on one side of the equation and then use logarithms to solve for the exponent.

5. Can I use a calculator to solve for exponents in proportionality?

Yes, you can use a calculator to solve for exponents in proportionality. Most scientific calculators have a logarithm function that you can use to find the value of an exponent. Just make sure to use the correct base when entering the equation into your calculator.

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