Problem with fractional exponents and negative numbers
12-08-2016, 04:53 PM
Post: #6
 Jan_D Member Posts: 69 Joined: Nov 2016
RE: Problem with fractional exponents and negative numbers
First we have to know how g^b is defined when b is not an integer.

So what would 0.47^3.1 be?

It is defined by means of the well-known functions e^x and ln(x), as follows:

g^b=e^[b*ln(g)]

This seems reasonable because e^[b*ln(g)]=e^[ln(g^b)]=g^b.

But when we use this definition in the case of g being negative we have to calculate the logarithm of a negative number, which does not exist within the realm of real numbers.

Within the realm of complex numbers such a logarithm exists though.

That is the reason why the result is a complex number, written as r+s*i, where r and s are real numbers, and i is the imaginary unit.
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 Messages In This Thread Problem with fractional exponents and negative numbers - German90 - 12-06-2016, 12:54 AM RE: Problem with fractional exponents and negative numbers - Han - 12-06-2016, 01:27 AM RE: Problem with fractional exponents and negative numbers - German90 - 12-06-2016, 01:44 AM RE: Problem with fractional exponents and negative numbers - Han - 12-06-2016, 05:33 AM RE: Problem with fractional exponents and negative numbers - Dirk.nl - 12-06-2016, 07:36 AM RE: Problem with fractional exponents and negative numbers - Jan_D - 12-08-2016 04:53 PM

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