Getal & Ruimte (12e editie) - havo wiskunde B
'Rekenen met logaritmen'.
| havo wiskunde B | 5.5 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 \({}^{5}\!\log(5)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 0ms b \({}^{5}\!\log(5) = {}^{5}\!\log(5^{1}) = 1\) 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 \({}^{9}\!\log(\frac{1}{81})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{9}\!\log(\frac{1}{81}) = {}^{9}\!\log(9^{-2}) = -2\) 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 \({}^{\frac{1}{9}}\!\log(81)\) Logaritme (6) 00fn - Rekenen met logaritmen - basis - 0ms b \({}^{\frac{1}{9}}\!\log({}^{\frac{1}{9}}\!\log(81)) = {}^{\frac{1}{9}}\!\log(\frac{1}{9}^{-2}) = -2\) 1p 1p c \({}^{2}\!\log(2 \sqrt{2})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{2}\!\log(2 \sqrt{2}) = {}^{2}\!\log(2^{1} ⋅ 2^{\frac{1}{2}}) = {}^{2}\!\log(2^{1\frac{1}{2}}) = 1\frac{1}{2}\) 1p 1p d \({}^{5}\!\log(5^{1{,}5})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{5}\!\log(5^{1{,}5}) = 1{,}5\) 1p |