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I'm a programmer working to write test software. Currently estimates the values it needs with by testing with a brute force algorithm. I'm trying to improve the math behind the software so that I can calculate the solution(s) instead. I seem to have come across an equation that is beyond my ability.

$(Bx_1 + 1)^{y_2}=(Bx_2 + 1)^{y_1}$

My goal is to have $B$ as a function of everything else, or have an algorithm solve for it. I feel like it should be possible, but I not even sure how to begin.

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    Oh yeah, I forgot about that property of $1$ and was just looking at it as a generic power. That would be the trivial answer but it is not the solution I need.2012-11-26

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Okay so I came up with a that allows me to approximate the answer if $\frac {y_2}{y_1}$ is rational (which it will be in my case because I have limited precision).

I can re-express the original equation as $(Bx_1+1)^{\frac {y_2}{y_1}}=Bx_2+1$

If $\frac {y_2}{y_1}$ rational I can change it to $\frac ND$ where $N$ and $D$ are integers. Substituting this back in and redistributing the fraction I get $(Bx_1+1)^N=(Bx_2+1)^D$

Here is the fun part, here I can do a binomial expansion on each side, this will give me one high-order polynomial that I can approximate the answer to. It's very messy but should get the job done.