Getal & Ruimte (12e editie) - vwo wiskunde B
'Rekenen met logaritmen'.
| vwo wiskunde B | 5.4 Logaritmen |
opgave 1Bereken. 1p a \({}^{8}\!\log(64)\) Logaritme (1) 00fi - Rekenen met logaritmen - basis - 0ms a \({}^{8}\!\log(64) = {}^{8}\!\log(8^{2}) = 2\) 1p 1p b \({}^{5}\!\log(5)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 0ms b \({}^{5}\!\log(5) = {}^{5}\!\log(5^{1}) = 1\) 1p 1p c \(\log(10)\) Logaritme (3) 00fk - Rekenen met logaritmen - basis - 0ms c \(\log(10) = \log(10^{1}) = 1\) 1p 1p d \({}^{8}\!\log(\frac{1}{64})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{8}\!\log(\frac{1}{64}) = {}^{8}\!\log(8^{-2}) = -2\) 1p opgave 2Bereken. 1p a \({}^{\frac{1}{6}}\!\log(\frac{1}{36})\) Logaritme (5) 00fm - Rekenen met logaritmen - basis - 0ms a \({}^{\frac{1}{6}}\!\log(\frac{1}{36}) = {}^{\frac{1}{6}}\!\log(\frac{1}{6}^{2}) = 2\) 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 \({}^{9}\!\log(9 \sqrt{9})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{9}\!\log(9 \sqrt{9}) = {}^{9}\!\log(9^{1} ⋅ 9^{\frac{1}{2}}) = {}^{9}\!\log(9^{1\frac{1}{2}}) = 1\frac{1}{2}\) 1p 1p d \({}^{4}\!\log(4^{7{,}9})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{4}\!\log(4^{7{,}9}) = 7{,}9\) 1p |