1. Stupid math question!

Is there a way to solve xx = c without just trial and error?

Backstory: Around 40 years ago another engineer and I at work were playing with our calculators. Those calculators had a maximum range of 9.99999999E99. If you hit one googol, out of range. Somehow we got wondering what was the largest number you could take to it's own power without going out of range. It took a couple of lunchtimes to get to the most digits we could put in. I still remember much of the number: 56.96124843, I think it was.

2. Those calculators don't do logs!

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I get about 56.96124 84322 60820 30512 22982 36945 72038 12195 56680 94908 79563 08808 98088 92097 88452 11000 doing a binary search. I don't what x is as a function of c.

4. Wow! Um, what's a binary search?

5. Originally Posted by Trebuchet
Wow! Um, what's a binary search?
See https://www.cs.cmu.edu/~rjsimmon/151...-binsearch.pdf

6. Originally Posted by Trebuchet
Wow! Um, what's a binary search?
Sort of a divide-and-conquer technique.

So take half the difference between your lower and upper bounds, 0.5, and add it to your lower bound. 56.5^56.5=9.789*10^98. Not enough, so 56.5 is now your lower bound.

So take half the difference between your lower and upper bounds, 0.25, and add it to your lower bound. 56.75^56.75=3.448*10^99. Not enough, so 56.75 is now your lower bound.

Fred

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