Machten
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Logaritmen
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M1
a^{0}=1
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L0
{}^a\log (b) + {}^a\log (c) = {}^a\log (b \cdot c)
{}^a\log (b) - {}^a\log (c) = {}^a\log (\frac{b}{c})
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M2
a^{1}=a
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L1
\begin{array}{l}
{}^a\log (b) = c \Rightarrow a^c = b \\
(a > 0 \wedge a \ne 1 \wedge b > 0) \\
\end{array}
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M3
a^{p}\cdot a^{q}=a^{p+q}
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L2
\begin{array}{l}
{}^a\log \left( b \right) = \frac{{\log \left( b \right)}}{{\log \left( a \right)}} \\
(zie\,\,*) \\
\end{array}
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M4
a^{p}:a^{q}=a^{p-q}
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L3
^a \log \left( {b^p } \right) = p \cdot {}^a\log (b)
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M5
(a^{p})^{q}=a^{p\cdot q}
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L4
a^{{}^a\log (b)} = b
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M6
(a\cdot b)^{p}=a^{p}\cdot b^{p}
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*)
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}
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M7
a^{-p}=\frac{1}{a^{p}}
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M8
a^{\frac{1}{2}}=\sqrt{a}
(a\ge 0)
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M9
\eqalign{
& {a^{\frac{p}{q}}} = \root q \of {{a^p}} \cr
& (a \ge 0) \cr}
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