Getal & Ruimte (12e editie) - vwo wiskunde A
'Rekenen met logaritmen'.
| vwo wiskunde A | 10.3 Logaritmen |
opgave 1Bereken. 1p a \({}^{6}\!\log(36)\) Logaritme (1) 00fi - Rekenen met logaritmen - basis - 0ms a \({}^{6}\!\log(36) = {}^{6}\!\log(6^{2}) = 2\) 1p 1p b \({}^{3}\!\log(1)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 0ms b \({}^{3}\!\log(1) = {}^{3}\!\log(3^{0}) = 0\) 1p 1p c \(\log(1\,000)\) Logaritme (3) 00fk - Rekenen met logaritmen - basis - 0ms c \(\log(1\,000) = \log(10^{3}) = 3\) 1p 1p d \({}^{7}\!\log(\frac{1}{49})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{7}\!\log(\frac{1}{49}) = {}^{7}\!\log(7^{-2}) = -2\) 1p opgave 2Bereken. 1p a \({}^{\frac{1}{9}}\!\log(\frac{1}{81})\) Logaritme (5) 00fm - Rekenen met logaritmen - basis - 0ms a \({}^{\frac{1}{9}}\!\log(\frac{1}{81}) = {}^{\frac{1}{9}}\!\log(\frac{1}{9}^{2}) = 2\) 1p 1p b \({}^{\frac{1}{6}}\!\log(36)\) Logaritme (6) 00fn - Rekenen met logaritmen - basis - 0ms b \({}^{\frac{1}{6}}\!\log({}^{\frac{1}{6}}\!\log(36)) = {}^{\frac{1}{6}}\!\log(\frac{1}{6}^{-2}) = -2\) 1p 1p c \({}^{6}\!\log(6 \sqrt{6})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{6}\!\log(6 \sqrt{6}) = {}^{6}\!\log(6^{1} ⋅ 6^{\frac{1}{2}}) = {}^{6}\!\log(6^{1\frac{1}{2}}) = 1\frac{1}{2}\) 1p 1p d \({}^{9}\!\log(9^{0{,}2})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{9}\!\log(9^{0{,}2}) = 0{,}2\) 1p |