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Proposition: Functional Equation of the Exponential Function of General Base

For all real \(x,y\in\mathbb R\), and all real \(a > 0\), the exponential function of general base \(a > 0 \) fulfills the following functional equation

\[\exp_a(x+y)=\exp_a(x)\cdot \exp_a(x).\]

Table of Contents

Proofs: 1 Corollaries: 1

Mentioned in:

Proofs: 1 2 3 4

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References

Bibliography

1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983