Getal & Ruimte (12e editie) - vwo wiskunde A
'Rekenen met logaritmen'.
| vwo wiskunde A | 10.3 Logaritmen |
opgave 1Bereken. 1p a \({}^{4}\!\log(16)\) Logaritme (1) 00fi - Rekenen met logaritmen - basis - 0ms a \({}^{4}\!\log(16) = {}^{4}\!\log(4^{2}) = 2\) 1p 1p b \({}^{8}\!\log(8)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 0ms b \({}^{8}\!\log(8) = {}^{8}\!\log(8^{1}) = 1\) 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 \({}^{8}\!\log(\frac{1}{8})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{8}\!\log(\frac{1}{8}) = {}^{8}\!\log(8^{-1}) = -1\) 1p opgave 2Bereken. 1p a \({}^{\frac{1}{7}}\!\log(\frac{1}{49})\) 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 \({}^{\frac{1}{6}}\!\log(36)\) 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 \({}^{7}\!\log(49 \sqrt{7})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{7}\!\log(49 \sqrt{7}) = {}^{7}\!\log(7^{2} ⋅ 7^{\frac{1}{2}}) = {}^{7}\!\log(7^{2\frac{1}{2}}) = 2\frac{1}{2}\) 1p 1p d \({}^{8}\!\log(8^{4{,}7})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{8}\!\log(8^{4{,}7}) = 4{,}7\) 1p |