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

[PDF] Rekenregels machten en logaritmen

©2004-2025 WisFaq