L0
${}^a\log (b) + {}^a\log (c) = {}^a\log (b \cdot c)$
${}^a\log (b) - {}^a\log (c) = {}^a\log (\frac{b}{c})$
L1
$\begin{array}{l}
{}^a\log (b) = c \Rightarrow a^c = b \\
(a > 0 \wedge a \ne 1 \wedge b > 0) \\
\end{array}$
L2
$\eqalign{\begin{array}{l}
{}^a\log \left( b \right) = \frac{{\log \left( b \right)}}{{\log \left( a \right)}} \\
(zie\,\,*) \\
\end{array}}$
L3
$^a \log \left( {b^p } \right) = p \cdot {}^a\log (b)$
L4
$a^{{}^a\log (b)} = b$
*)
L2 uitgebreid
$\eqalign{\begin{array}{l}
{}^a\log \left( b \right) = \frac{{{}^g\log \left( b \right)}}{{{}^g\log \left( a \right)}} \\
(g > 0) \\
\end{array}}$