Getal & Ruimte (12e editie) - vwo wiskunde B
'Rekenen met logaritmen'.
| vwo wiskunde B | 5.4 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 \({}^{4}\!\log(4)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 0ms b \({}^{4}\!\log(4) = {}^{4}\!\log(4^{1}) = 1\) 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 \({}^{8}\!\log(\frac{1}{8})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{8}\!\log(\frac{1}{8}) = {}^{8}\!\log(8^{-1}) = -1\) 1p opgave 2Bereken. 1p a \({}^{\frac{1}{3}}\!\log(\frac{1}{27})\) Logaritme (5) 00fm - Rekenen met logaritmen - basis - 0ms a \({}^{\frac{1}{3}}\!\log(\frac{1}{27}) = {}^{\frac{1}{3}}\!\log(\frac{1}{3}^{3}) = 3\) 1p 1p b \({}^{\frac{1}{5}}\!\log(25)\) Logaritme (6) 00fn - Rekenen met logaritmen - basis - 0ms b \({}^{\frac{1}{5}}\!\log({}^{\frac{1}{5}}\!\log(25)) = {}^{\frac{1}{5}}\!\log(\frac{1}{5}^{-2}) = -2\) 1p 1p c \({}^{9}\!\log(81 \sqrt{9})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{9}\!\log(81 \sqrt{9}) = {}^{9}\!\log(9^{2} ⋅ 9^{\frac{1}{2}}) = {}^{9}\!\log(9^{2\frac{1}{2}}) = 2\frac{1}{2}\) 1p 1p d \({}^{4}\!\log(4^{4{,}2})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{4}\!\log(4^{4{,}2}) = 4{,}2\) 1p |