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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