Getal & Ruimte (13e editie) - vwo wiskunde B
'Rekenen met logaritmen'.
| vwo wiskunde B | 5.5 Logaritmen |
opgave 1Bereken. 1p a \({}^{4}\!\log(16)\) Logaritme (1) 00fi - Rekenen met logaritmen - basis - 0ms a \({}^{4}\!\log(16) = {}^{4}\!\log(4^{2}) = 2\) 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 \(\log(100)\) Logaritme (3) 00fk - Rekenen met logaritmen - basis - 0ms c \(\log(100) = \log(10^{2}) = 2\) 1p 1p d \({}^{5}\!\log(\frac{1}{25})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{5}\!\log(\frac{1}{25}) = {}^{5}\!\log(5^{-2}) = -2\) 1p opgave 2Bereken. 1p a \({}^{\frac{1}{4}}\!\log(\frac{1}{64})\) Logaritme (5) 00fm - Rekenen met logaritmen - basis - 0ms a \({}^{\frac{1}{4}}\!\log(\frac{1}{64}) = {}^{\frac{1}{4}}\!\log(\frac{1}{4}^{3}) = 3\) 1p 1p b \({}^{\frac{1}{2}}\!\log(16)\) Logaritme (6) 00fn - Rekenen met logaritmen - basis - 0ms b \({}^{\frac{1}{2}}\!\log({}^{\frac{1}{2}}\!\log(16)) = {}^{\frac{1}{2}}\!\log(\frac{1}{2}^{-4}) = -4\) 1p 1p c \({}^{8}\!\log(8 \sqrt{8})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{8}\!\log(8 \sqrt{8}) = {}^{8}\!\log(8^{1} ⋅ 8^{\frac{1}{2}}) = {}^{8}\!\log(8^{1\frac{1}{2}}) = 1\frac{1}{2}\) 1p 1p d \({}^{6}\!\log(6^{2{,}6})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{6}\!\log(6^{2{,}6}) = 2{,}6\) 1p |