Getal & Ruimte (12e editie) - vwo wiskunde A
'Rekenen met logaritmen'.
| vwo wiskunde A | 10.3 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 \({}^{7}\!\log(1)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 0ms b \({}^{7}\!\log(1) = {}^{7}\!\log(7^{0}) = 0\) 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 \({}^{2}\!\log(\frac{1}{32})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{2}\!\log(\frac{1}{32}) = {}^{2}\!\log(2^{-5}) = -5\) 1p opgave 2Bereken. 1p a \({}^{\frac{1}{8}}\!\log(\frac{1}{64})\) Logaritme (5) 00fm - Rekenen met logaritmen - basis - 0ms a \({}^{\frac{1}{8}}\!\log(\frac{1}{64}) = {}^{\frac{1}{8}}\!\log(\frac{1}{8}^{2}) = 2\) 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 \({}^{4}\!\log(16 \sqrt{4})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{4}\!\log(16 \sqrt{4}) = {}^{4}\!\log(4^{2} ⋅ 4^{\frac{1}{2}}) = {}^{4}\!\log(4^{2\frac{1}{2}}) = 2\frac{1}{2}\) 1p 1p d \({}^{9}\!\log(9^{6{,}8})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{9}\!\log(9^{6{,}8}) = 6{,}8\) 1p |