Rekenregels voor machten en logaritmen

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} $	© 2016 WisFaq.nl

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