Transcendental Function/Examples/Logarithm Functions

Examples of Transcendental Functions

The logarithm functions are transcendental.

Real Logarithm Function is Transcendental

Real Logarithm Function is Transcendental

Complex Logarithm Function is Transcendental

Let $a \in \R_{>0}$ be a strictly positive real number such that $a \ne 1$.

Let $\log_a: \C \to \C$ denote the complex general logarithm base $a$.

$\log_a$ is a transcendental function.

Sources

• 1973: G. Stephenson: Mathematical Methods for Science Students (2nd ed.) ... (previous) ... (next): Chapter $1$: Real Numbers and Functions of a Real Variable: $1.3$ Functions of a Real Variable: $\text {(g)}$ Transcendental Functions
• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $2$: Functions, Limits and Continuity: The Elementary Functions: $10$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): function (map, mapping)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): function (map, mapping)