Getal & Ruimte (12e editie) - havo wiskunde B
'Rekenen met logaritmen'.
| havo wiskunde B | 5.5 Logaritmen |
opgave 1Bereken. 1p a \({}^{3}\!\log(9)\) Logaritme (1) 00fi - Rekenen met logaritmen - basis - 0ms a \({}^{3}\!\log(9) = {}^{3}\!\log(3^{2}) = 2\) 1p 1p b \({}^{3}\!\log(1)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 0ms b \({}^{3}\!\log(1) = {}^{3}\!\log(3^{0}) = 0\) 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 \({}^{4}\!\log(\frac{1}{16})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{4}\!\log(\frac{1}{16}) = {}^{4}\!\log(4^{-2}) = -2\) 1p opgave 2Bereken. 1p a \({}^{\frac{1}{5}}\!\log(\frac{1}{125})\) Logaritme (5) 00fm - Rekenen met logaritmen - basis - 0ms a \({}^{\frac{1}{5}}\!\log(\frac{1}{125}) = {}^{\frac{1}{5}}\!\log(\frac{1}{5}^{3}) = 3\) 1p 1p b \({}^{\frac{1}{6}}\!\log(36)\) Logaritme (6) 00fn - Rekenen met logaritmen - basis - 0ms b \({}^{\frac{1}{6}}\!\log({}^{\frac{1}{6}}\!\log(36)) = {}^{\frac{1}{6}}\!\log(\frac{1}{6}^{-2}) = -2\) 1p 1p c \({}^{2}\!\log(32 \sqrt{2})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{2}\!\log(32 \sqrt{2}) = {}^{2}\!\log(2^{5} ⋅ 2^{\frac{1}{2}}) = {}^{2}\!\log(2^{5\frac{1}{2}}) = 5\frac{1}{2}\) 1p 1p d \({}^{4}\!\log(4^{2{,}7})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{4}\!\log(4^{2{,}7}) = 2{,}7\) 1p |