# Category:Natural Logarithms

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This category contains results about **Natural Logarithms**.

### Positive Real Numbers

Let $x \in \R$ be a real number such that $x > 0$.

The **(natural) logarithm** of $x$ is defined as:

- $\ds \ln x := \int_1^x \frac {\d t} t$

### 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 the following 9 subcategories, out of 9 total.

### D

### E

### N

### U

## Pages in category "Natural Logarithms"

The following 25 pages are in this category, out of 25 total.

### D

- Defining Sequence of Natural Logarithm is Convergent
- Defining Sequence of Natural Logarithm is Strictly Decreasing
- Defining Sequence of Natural Logarithm is Uniformly Convergent on Compact Sets
- Derivative of Natural Logarithm Function
- Difference between Summation of Natural Logarithms and Summation of Harmonic Numbers
- Domain of Real Natural Logarithm