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

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The discussion centers on the requirement for the base b in the exponential function f(x)=ab^{x} to be a positive real number. Participants explore the implications of using a negative base, noting that it leads to complex numbers, such as when b = -1 and x = 1/2 results in the square root of -1. The consensus is that since complex numbers are not applicable in this context, the base must remain positive and real. This ensures the function behaves predictably and remains within the realm of real numbers. The conversation concludes with an acknowledgment of the transition into complex numbers when the base is not positive.
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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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