Getal & Ruimte (12e editie) - vwo wiskunde B
'Rekenen met logaritmen'.
| vwo wiskunde B | 5.4 Logaritmen |
opgave 1Bereken. 1p a \({}^{9}\!\log(81)\) Logaritme (1) 00fi - Rekenen met logaritmen - basis - 0ms a \({}^{9}\!\log(81) = {}^{9}\!\log(9^{2}) = 2\) 1p 1p b \({}^{5}\!\log(1)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 0ms b \({}^{5}\!\log(1) = {}^{5}\!\log(5^{0}) = 0\) 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 \({}^{5}\!\log(\frac{1}{125})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{5}\!\log(\frac{1}{125}) = {}^{5}\!\log(5^{-3}) = -3\) 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 \({}^{\frac{1}{5}}\!\log(125)\) Logaritme (6) 00fn - Rekenen met logaritmen - basis - 0ms b \({}^{\frac{1}{5}}\!\log({}^{\frac{1}{5}}\!\log(125)) = {}^{\frac{1}{5}}\!\log(\frac{1}{5}^{-3}) = -3\) 1p 1p c \({}^{3}\!\log(27 \sqrt{3})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{3}\!\log(27 \sqrt{3}) = {}^{3}\!\log(3^{3} ⋅ 3^{\frac{1}{2}}) = {}^{3}\!\log(3^{3\frac{1}{2}}) = 3\frac{1}{2}\) 1p 1p d \({}^{9}\!\log(9^{1{,}3})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{9}\!\log(9^{1{,}3}) = 1{,}3\) 1p |