Category:Examples of Natural Logarithms
Jump to navigation
Jump to search
This category contains examples of Natural Logarithm.
Positive Real Numbers
The (natural) logarithm of $x$ is the real-valued function defined on $\R_{>0}$ as:
- $\ds \forall x \in \R_{>0}: \ln x := \int_1^x \frac {\d t} t$
Complex Numbers
Let $z = r e^{i \theta}$ be a complex number expressed in exponential form such that $z \ne 0$.
The complex natural logarithm of $z \in \C_{\ne 0}$ is the multifunction defined as:
- $\map \ln z := \set {\map \ln r + i \paren {\theta + 2 k \pi}: k \in \Z}$
where $\map \ln r$ is the natural logarithm of the (strictly) positive real number $r$.
Subcategories
This category has only the following subcategory.
N
- Natural Logarithm of 1 is 0 (4 P)
Pages in category "Examples of Natural Logarithms"
The following 12 pages are in this category, out of 12 total.