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Properties of Logarithms

Definition 1.1. Logarithm: $x = a^{y} \Leftrightarrow y = \log_{a} x$ .

Properties

$\log_{a} 1 = 0$
$\log_{a} a^{x} = x$
$a^{\log_{a} x} = x$
$\log_{a} (M N) = \log_{a} M + \log_{a} N$
$\log_{a} (\frac{M}{N}) = \log_{a} M - \log_{a} N$
$\log_{a} (M^{c}) = c \log_{a} M$
$\log_{a} x = \frac{\log_{b} x}{\log_{b} a}$

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Last revised: 17 March 2005 12:45 p.m.