Getal & Ruimte (12e editie) - havo wiskunde B
'Rekenen met logaritmen'.
| havo wiskunde B | 5.5 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 \({}^{9}\!\log(1)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 0ms b \({}^{9}\!\log(1) = {}^{9}\!\log(9^{0}) = 0\) 1p 1p c \(\log(10)\) Logaritme (3) 00fk - Rekenen met logaritmen - basis - 0ms c \(\log(10) = \log(10^{1}) = 1\) 1p 1p d \({}^{5}\!\log(\frac{1}{5})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{5}\!\log(\frac{1}{5}) = {}^{5}\!\log(5^{-1}) = -1\) 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 \({}^{\frac{1}{8}}\!\log(64)\) Logaritme (6) 00fn - Rekenen met logaritmen - basis - 0ms b \({}^{\frac{1}{8}}\!\log({}^{\frac{1}{8}}\!\log(64)) = {}^{\frac{1}{8}}\!\log(\frac{1}{8}^{-2}) = -2\) 1p 1p c \({}^{8}\!\log(64 \sqrt{8})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{8}\!\log(64 \sqrt{8}) = {}^{8}\!\log(8^{2} ⋅ 8^{\frac{1}{2}}) = {}^{8}\!\log(8^{2\frac{1}{2}}) = 2\frac{1}{2}\) 1p 1p d \({}^{5}\!\log(5^{1{,}2})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{5}\!\log(5^{1{,}2}) = 1{,}2\) 1p |