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Mathematics-Online lexicon:

Calculation Rules for Power and Logarithm

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From the definition and the functional equalities of the exponential and logarithmic function follows

\begin{displaymath} \begin{array}{rclrcl} a^{s+t} &=& a^s \,a^t,\quad & \log_a ... ...t &=& a^{st}\,\quad & \log_a x^t &=& t \log_a x\, . \end{array}\end{displaymath}

Furthermore holds

$\displaystyle \log_b a\,\log_a x = \log_b x\, . $

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  automatically generated 4/ 8/2008