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Raising a number to a non-integer power.

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TimFox:
No, your definition only works for real numbers, using the limit of a sequence of rational numbers to deal with the irrational case.
The logarithm method also works for complex numbers.

Nominal Animal:
Actually, the form ab = 2b log2 a is useful, as it is something a computer can do in binary directly, and quite efficiently for base-2 floating point numbers. Details.

vk6zgo:
From 30+ years ago (& it was revision then), the classic formula for fractional indices is a^p/q = the qth root of  a^p
I was hoping to use the calculator, but the HP22S doesn't seen to have the capability of powers or roots to other than base 2 or e.

I could use the logs, but to hell with it!

magic:

--- Quote from: TimFox on May 28, 2020, 02:54:58 am ---No, your definition only works for real numbers, using the limit of a sequence of rational numbers to deal with the irrational case.
The logarithm method also works for complex numbers.

--- End quote ---
Fair enough, off the top of my head I can't provide a simple algebraic argument why complex exponents should be defined the way they are. That doesn't necessarily mean no such argument exists. I don't know what reasoning originally led to the Euler identity and things like that - perhaps the Taylor series, maybe something more direct and straightforward.

That being said, I totally expected OP to stop reading at the first limit if he even made it that far, so who cares about C ;)

TimFox:
In my youth, if I needed more accuracy than from my slide rule, I used 5-place logarithm tables (and log-trig tables) to do my serious computations, so the logarithm definition comes naturally to me.   We referred to the Chemical Rubber Company "Handbook of Mathematical Tables" as the Rubber Bible.  (Formally, the "Mathematical Tables from the Handbook of Chemistry and Physics")  7-place tables were available, but that was overkill.

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