Category:Examples of General 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.