Getal & Ruimte (12e editie) - havo wiskunde B
'Rekenen met logaritmen'.
| havo wiskunde B | 5.5 Logaritmen |
opgave 1Bereken. 1p a \({}^{5}\!\log(25)\) Logaritme (1) 00fi - Rekenen met logaritmen - basis - 0ms a \({}^{5}\!\log(25) = {}^{5}\!\log(5^{2}) = 2\) 1p 1p b \({}^{8}\!\log(1)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 0ms b \({}^{8}\!\log(1) = {}^{8}\!\log(8^{0}) = 0\) 1p 1p c \(\log(100\,000)\) Logaritme (3) 00fk - Rekenen met logaritmen - basis - 0ms c \(\log(100\,000) = \log(10^{5}) = 5\) 1p 1p d \({}^{3}\!\log(\frac{1}{3})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{3}\!\log(\frac{1}{3}) = {}^{3}\!\log(3^{-1}) = -1\) 1p opgave 2Bereken. 1p a \({}^{\frac{1}{7}}\!\log(\frac{1}{49})\) Logaritme (5) 00fm - Rekenen met logaritmen - basis - 0ms a \({}^{\frac{1}{7}}\!\log(\frac{1}{49}) = {}^{\frac{1}{7}}\!\log(\frac{1}{7}^{2}) = 2\) 1p 1p b \({}^{\frac{1}{2}}\!\log(16)\) Logaritme (6) 00fn - Rekenen met logaritmen - basis - 0ms b \({}^{\frac{1}{2}}\!\log({}^{\frac{1}{2}}\!\log(16)) = {}^{\frac{1}{2}}\!\log(\frac{1}{2}^{-4}) = -4\) 1p 1p c \({}^{5}\!\log(125 \sqrt{5})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{5}\!\log(125 \sqrt{5}) = {}^{5}\!\log(5^{3} ⋅ 5^{\frac{1}{2}}) = {}^{5}\!\log(5^{3\frac{1}{2}}) = 3\frac{1}{2}\) 1p 1p d \({}^{7}\!\log(7^{7{,}6})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{7}\!\log(7^{7{,}6}) = 7{,}6\) 1p |