The problem I'm facing is solving the following equation for $p$ given the constants $a_i$ and $b_i$:
$ \sum_i \frac{a_i}{b_i^p} = 1 $
Is there a general technique that would allow me to find a value for $p$? If not, are there any heuristic approaches that do not require a computer I can use to find a value for $p$?