---
tag: 02YSJPQYQH
kind: concept
name: Branch of the logarithm
aliases: [branch-of-log, logarithm-branch]
msc: [33B10]
sources:
  - url: https://en.wikipedia.org/wiki/Complex_logarithm
    locator: Branches of the complex logarithm
---

## Summary

A branch of the logarithm on an open set $U \subseteq \mathbb{C} \setminus \{0\}$ is a continuous function $L$ on $U$ with $e^{L(z)} = z$, see the [[definition|0SQ1F2BEDS]].
On a domain, two branches differ by a constant integer multiple of $2\pi i$.