Machten

Logaritmen

M1
$a^{0}=1$

L0
${}^a\log (b) + {}^a\log (c) = {}^a\log (b \cdot c)$

${}^a\log (b) - {}^a\log (c) = {}^a\log (\frac{b}{c})$

M2
$a^{1}=a$

L1
$\begin{array}{l}
{}^a\log (b) = c \Rightarrow a^c = b \\
(a > 0 \wedge a \ne 1 \wedge b > 0) \\
\end{array}$

M3
$a^{p}\cdot a^{q}=a^{p+q}$

L2
$\begin{array}{l}
{}^a\log \left( b \right) = \frac{{\log \left( b \right)}}{{\log \left( a \right)}} \\
(zie\,\,*) \\
\end{array}$

M4
$a^{p}:a^{q}=a^{p-q}$

L3
$^a \log \left( {b^p } \right) = p \cdot {}^a\log (b)$

M5
$(a^{p})^{q}=a^{p\cdot q}$

L4
$a^{{}^a\log (b)} = b$

M6
$(a\cdot b)^{p}=a^{p}\cdot b^{p}$

*)
L2 uitgebreid
$\begin{array}{l}
{}^a\log \left( b \right) = \frac{{{}^g\log \left( b \right)}}{{{}^g\log \left( a \right)}} \\
(g > 0) \\
\end{array}$

M7
$a^{-p}=\frac{1}{a^{p}}$

M8
$a^{\frac{1}{2}}=\sqrt{a}$
$(a\ge 0)$

M9
$\eqalign{
  & {a^{\frac{p}{q}}} = \root q \of {{a^p}}   \cr
  & (a \ge 0) \cr} $

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