Getal & Ruimte (12e editie) - vwo wiskunde A
'Rekenen met logaritmen'.
| vwo wiskunde A | 10.3 Logaritmen |
opgave 1Bereken. 1p a \({}^{2}\!\log(8)\) Logaritme (1) 00fi - Rekenen met logaritmen - basis - 0ms a \({}^{2}\!\log(8) = {}^{2}\!\log(2^{3}) = 3\) 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 \(\log(1\,000)\) Logaritme (3) 00fk - Rekenen met logaritmen - basis - 0ms c \(\log(1\,000) = \log(10^{3}) = 3\) 1p 1p d \({}^{9}\!\log(\frac{1}{9})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{9}\!\log(\frac{1}{9}) = {}^{9}\!\log(9^{-1}) = -1\) 1p opgave 2Bereken. 1p a \({}^{\frac{1}{10}}\!\log(\frac{1}{100})\) Logaritme (5) 00fm - Rekenen met logaritmen - basis - 0ms a \({}^{\frac{1}{10}}\!\log(\frac{1}{100}) = {}^{\frac{1}{10}}\!\log(\frac{1}{10}^{2}) = 2\) 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 \({}^{3}\!\log(3 \sqrt{3})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{3}\!\log(3 \sqrt{3}) = {}^{3}\!\log(3^{1} ⋅ 3^{\frac{1}{2}}) = {}^{3}\!\log(3^{1\frac{1}{2}}) = 1\frac{1}{2}\) 1p 1p d \({}^{2}\!\log(2^{8{,}9})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{2}\!\log(2^{8{,}9}) = 8{,}9\) 1p |