F(x)=ab^{x} where b must be a positive real number

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The discussion centers on the mathematical definition of exponential functions, specifically the form F(x) = ab^x, where b must be a positive real number. Participants clarify that using a negative base, such as b < 0 or b = -1, leads to complex numbers, which are not applicable in this context. The necessity for b to be positive and real ensures the function remains within the realm of real numbers, avoiding complications with imaginary units like i.

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Quote: "In mathematics, an exponential function is a function of the form

f(x)=ab^{x}

where b is a POSITIVE REAL number"

Wait. Give me a reason, why exponent base must be positive and real?

What happens if b<0?
 
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Avalance789 said:
Quote: "In mathematics, an exponential function is a function of the form

f(x)=ab^{x}

where b is a POSITIVE REAL number"

Wait. Give me a reason, why exponent base must be positive and real?

What happens if b<0?
What happens if b = -1 and x = 1/2?

-Dan
 
It means sqrt{-1}?

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Avalance789 said:
It means sqrt{-1}?

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Exactly. And as i is not real number we can't use it for what you seem to be working with.

-Dan
 
Ok, got it. So from this point we get into complex numbers.

Thank you!

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