Getal & Ruimte (12e editie) - vwo wiskunde A
'Rekenen met logaritmen'.
| vwo wiskunde A | 10.3 Logaritmen |
opgave 1Bereken. 1p a \({}^{3}\!\log(81)\) Logaritme (1) 00fi - Rekenen met logaritmen - basis - 0ms a \({}^{3}\!\log(81) = {}^{3}\!\log(3^{4}) = 4\) 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 \(\log(1\,000\,000)\) Logaritme (3) 00fk - Rekenen met logaritmen - basis - 0ms c \(\log(1\,000\,000) = \log(10^{6}) = 6\) 1p 1p d \({}^{6}\!\log(\frac{1}{36})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{6}\!\log(\frac{1}{36}) = {}^{6}\!\log(6^{-2}) = -2\) 1p opgave 2Bereken. 1p a \({}^{\frac{1}{9}}\!\log(\frac{1}{81})\) Logaritme (5) 00fm - Rekenen met logaritmen - basis - 0ms a \({}^{\frac{1}{9}}\!\log(\frac{1}{81}) = {}^{\frac{1}{9}}\!\log(\frac{1}{9}^{2}) = 2\) 1p 1p b \({}^{\frac{1}{2}}\!\log(8)\) Logaritme (6) 00fn - Rekenen met logaritmen - basis - 0ms b \({}^{\frac{1}{2}}\!\log({}^{\frac{1}{2}}\!\log(8)) = {}^{\frac{1}{2}}\!\log(\frac{1}{2}^{-3}) = -3\) 1p 1p c \({}^{4}\!\log(4 \sqrt{4})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{4}\!\log(4 \sqrt{4}) = {}^{4}\!\log(4^{1} ⋅ 4^{\frac{1}{2}}) = {}^{4}\!\log(4^{1\frac{1}{2}}) = 1\frac{1}{2}\) 1p 1p d \({}^{7}\!\log(7^{4{,}6})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{7}\!\log(7^{4{,}6}) = 4{,}6\) 1p |