I see that no one is up to that challenge. let me answer this myself:
2^1.3 is "a little" less than 2^1.5, which is about 1.4 cubed, so that is 1.96 times 1.4, so about 2.8
I I would say 2.6 is a good guess.
try newton's method. you are looking for the root to 2^13=x^10 guess a root then follow the algorithm
it sounds stupid and tedius but it should be easy to code
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