Category:Examples of Logarithms
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This category contains examples of General Logarithm.
Positive Real Numbers
Let $x \in \R_{>0}$ be a strictly positive real number.
Let $a \in \R_{>0}$ be a strictly positive real number such that $a \ne 1$.
The logarithm to the base $a$ of $x$ is defined as:
- $\log_a x := y \in \R: a^y = x$
where $a^y = e^{y \ln a}$ as defined in Powers of Real Numbers.
Complex Numbers
Let $z \in \C_{\ne 0}$ be a non-zero complex number.
Let $a \in \R_{>0}$ be a strictly positive real number such that $a \ne 1$.
The logarithm to the base $a$ of $z$ is defined as:
- $\log_a z := \set {y \in \C: a^y = z}$
where $a^y = e^{y \ln a}$ as defined in Powers of Complex Numbers.
Subcategories
This category has the following 5 subcategories, out of 5 total.
E
- Examples of Common Logarithms (21 P)