# Definition:Natural Logarithm/Notation

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## Definition

The notation for the **natural logarithm function** is misleadingly inconsistent throughout the literature. It is written variously as:

- $\ln z$
- $\log z$
- $\Log z$
- $\log_e z$

The first of these is commonly encountered, and is the preferred form on $\mathsf{Pr} \infty \mathsf{fWiki}$. However, many who consider themselves serious mathematicians believe this notation to be unsophisticated.

The second and third are ambiguous (it doesn't tell you which base it is the logarithm of).

While the fourth option is more verbose than the others, there is no confusion about exactly what is meant.

## Sources

- 1988: Dominic Welsh:
*Codes and Cryptography*... (previous) ... (next): Notation - 1992: Larry C. Andrews:
*Special Functions of Mathematics for Engineers*(2nd ed.) ... (previous) ... (next): $\S 1.2.2$: Summary of convergence tests (footnote) - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**logarithm (log)** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**logarithm (log)**