◀ ▲ ▶Branches / Analysis / Definition: Exponential Function of General Base
Definition: Exponential Function of General Base
Let \(a > 0\) be a positive real number, and let \(\ln(a)\) be the natural logarithm of \(a\). The exponential function of general base \(a\) is defined as the exponential function:
\[a^x:=\exp_a(x):=\begin{cases}\mathbb R&\mapsto \mathbb R\\x&\mapsto \exp(x\cdot \ln(a)).\end{cases}\]
Table of Contents
 Proposition: Continuity of Exponential Function of General Base
 Proposition: Functional Equation of the Exponential Function of General Base
 Proposition: Exponential Function of General Base With Natural Exponents
 Proposition: Exponential Function of General Base With Integer Exponents
 Proposition: Functional Equation of the Exponential Function of General Base (Revised)
Mentioned in:
Corollaries: 1
Proofs: 2 3 4 5 6 7 8
Propositions: 9 10 11 12 13 14 15 16
Thank you to the contributors under CC BYSA 4.0!
 Github:

References
Bibliography
 Forster Otto: "Analysis 1, Differential und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983