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 \({}^{5}\!\log(5)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 0ms b \({}^{5}\!\log(5) = {}^{5}\!\log(5^{1}) = 1\) 1p 1p c \(\log(100\,000)\) Logaritme (3) 00fk - Rekenen met logaritmen - basis - 0ms c \(\log(100\,000) = \log(10^{5}) = 5\) 1p 1p d \({}^{2}\!\log(\frac{1}{32})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{2}\!\log(\frac{1}{32}) = {}^{2}\!\log(2^{-5}) = -5\) 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 \({}^{\frac{1}{9}}\!\log(81)\) Logaritme (6) 00fn - Rekenen met logaritmen - basis - 0ms b \({}^{\frac{1}{9}}\!\log({}^{\frac{1}{9}}\!\log(81)) = {}^{\frac{1}{9}}\!\log(\frac{1}{9}^{-2}) = -2\) 1p 1p c \({}^{4}\!\log(64 \sqrt{4})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{4}\!\log(64 \sqrt{4}) = {}^{4}\!\log(4^{3} ⋅ 4^{\frac{1}{2}}) = {}^{4}\!\log(4^{3\frac{1}{2}}) = 3\frac{1}{2}\) 1p 1p d \({}^{4}\!\log(4^{2{,}1})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{4}\!\log(4^{2{,}1}) = 2{,}1\) 1p |