matching a multi-variable function with 2 bounded unknown variables to a value with graphical representation

Question

My question is about matching this function: N = 0.13*(s^a), where s and a are variables, to a value. I am trying to find all values of s and a that satisfy N = 100 and N = 10,000,000. S is bounded from 0 to 101 and a is bounded from 3 to 8. And I would like to visualize the results possibly by graphing it with the axes being s and a, like a 2D plot. The algorithms I found that were similar to what I need seemed to all want to find the minimum or maximum of a function instead of matching it to a value. I have hit a wall and I don't know if my coding skills are high enough to write my own algorithm. Any help would be greatly appreciated! Thanks in advance!

Answer 1

This can easily be converted to a minimization problem. Simply minimize this function:

abs(0.13 * s ^ a - 100)

Replace the 100 with 10,000,000 for the second part. It will take some modification to find all values of s and a , rather than just one pair. This could be done by fixing an s value and minimizing over a , then repeating for different s values.