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Mathematics-Online course: Prepcourse Mathematics - Analysis - Functions

Exponential and Logarithm Functions

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For $ a>0$ define

$\displaystyle y=a^x = \exp (x\ln a) $

with its inverse function

$\displaystyle x=\log_a y,\quad y>0.$

In particular, the abbreviations $ \log=\log_{10}$ and $ \operatorname{ld} = \log_2$ are commonly used for the logarithm to the base $ 10$ and for the dual logarithm respectively.
\includegraphics[height=5cm]{a_allg_logarithmus_bild1.eps}   \includegraphics[height=5cm]{a_allg_logarithmus_bild2.eps}
$ f(x)=2^x$   $ f(x)= \operatorname{ld}(x)$

(Authors: Höllig/Kopf/Abele)
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  automatically generated 9/18/2007