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Logarithm

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Definition

\begin{matrix} \log_{b} x = y \\ such that \\ x = b^{y} \end{matrix}

For any $x, y, b \in ℝ^{+}$ where $b \neq 1$ ,

\begin{matrix} \log_{b} x y = \log_{b} x + \log_{b} y . \end{matrix}

Equivalently, for quotients,

\begin{matrix} \log_{b} (\frac{x}{y}) = \log_{b} x - \log_{b} y . \end{matrix}

$l o g_{b} m^{n} = n l o g_{b} m$