If you decide to research specialized algorithms for calculating logs with a variety of bases, it may make sense to start trying to add one to the numeric-functions package [*] before going for base. Aleksey Khudyakov has been doing a lot of work on that package of late, and would likely be able to help you work out potential issues.
[*] https://hackage.haskell.org/package/math-functions
And that's why non-experts like me should not be let near the actual implementation.
Thank you very much for all the detailed information and for purging some of the falsehoods in my worldview. I knew that I misunderstood a lot of stuff but now I have a better picture of were the errors actually are.
So again, thanks!
MarLinn
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