Getal & Ruimte (12e editie) - vwo wiskunde A
'Rekenen met logaritmen'.
| vwo wiskunde A | 10.3 Logaritmen |
opgave 1Bereken. 1p a \({}^{3}\!\log(27)\) Logaritme (1) 00fi - Rekenen met logaritmen - basis - 0ms a \({}^{3}\!\log(27) = {}^{3}\!\log(3^{3}) = 3\) 1p 1p b \({}^{2}\!\log(2)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 0ms b \({}^{2}\!\log(2) = {}^{2}\!\log(2^{1}) = 1\) 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 \({}^{9}\!\log(\frac{1}{9})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{9}\!\log(\frac{1}{9}) = {}^{9}\!\log(9^{-1}) = -1\) 1p opgave 2Bereken. 1p a \({}^{\frac{1}{6}}\!\log(\frac{1}{36})\) Logaritme (5) 00fm - Rekenen met logaritmen - basis - 0ms a \({}^{\frac{1}{6}}\!\log(\frac{1}{36}) = {}^{\frac{1}{6}}\!\log(\frac{1}{6}^{2}) = 2\) 1p 1p b \({}^{\frac{1}{4}}\!\log(16)\) Logaritme (6) 00fn - Rekenen met logaritmen - basis - 0ms b \({}^{\frac{1}{4}}\!\log({}^{\frac{1}{4}}\!\log(16)) = {}^{\frac{1}{4}}\!\log(\frac{1}{4}^{-2}) = -2\) 1p 1p c \({}^{6}\!\log(6 \sqrt{6})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{6}\!\log(6 \sqrt{6}) = {}^{6}\!\log(6^{1} ⋅ 6^{\frac{1}{2}}) = {}^{6}\!\log(6^{1\frac{1}{2}}) = 1\frac{1}{2}\) 1p 1p d \({}^{4}\!\log(4^{3{,}3})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{4}\!\log(4^{3{,}3}) = 3{,}3\) 1p |