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Subject: "Esponential Proof"     Previous Topic | Next Topic
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Conferences The CTK Exchange College math Topic #438
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Marcos Mothé
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Apr-05-04, 12:04 PM (EST)
 
"Esponential Proof"
 
   Someone knows how could I proof that only the exponential function follows that f(a+b)=f(a)*f(b)?


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alexbadmin
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1239 posts
Apr-05-04, 12:45 PM (EST)
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1. "RE: Esponential Proof"
In response to message #0
 
   >Someone knows how could I proof that only the exponential
>function follows that f(a+b)=f(a)*f(b)?

This is only true if the function f is assumed to be continuous and defined for all reals. Please note that, if g(x) = log(f(x)) (and the definition makes sense, i.e., if f(x) is positive) then

g(a + b) = g(a) + g(b).

For the latter see https://www.cut-the-knot.org/do_you_know/linear.shtml


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