Mathematics-Online lexicon: Logarithmic Function

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	Mathematics-Online lexicon:
	Logarithmic Function

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

The logarithmic function is the inverse function of the exponential function:

$\displaystyle y=e^x \quad\Leftrightarrow\quad x=\ln y .$

$\includegraphics[width=7.4cm]{graph_logarithmus}$

It maps $(0,\infty)$ monotone on $\mathbb{R}$ and satisfies the functional equality

$\displaystyle \ln(xy) = \ln x + \ln y .$

In particular $\ln (1/x)=-\ln x$ .

Examples:

automatically generated 4/ 8/2008