Problem with fractional exponents and negative numbers

12082016, 04:53 PM
Post: #6




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 wellknown 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  12062016, 12:54 AM
RE: Problem with fractional exponents and negative numbers  Han  12062016, 01:27 AM
RE: Problem with fractional exponents and negative numbers  German90  12062016, 01:44 AM
RE: Problem with fractional exponents and negative numbers  Han  12062016, 05:33 AM
RE: Problem with fractional exponents and negative numbers  Dirk.nl  12062016, 07:36 AM
RE: Problem with fractional exponents and negative numbers  Jan_D  12082016 04:53 PM

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