Getal & Ruimte (12e editie) - vwo wiskunde A
'Rekenen met logaritmen'.
| vwo wiskunde A | 10.3 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 \({}^{4}\!\log(4)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 0ms b \({}^{4}\!\log(4) = {}^{4}\!\log(4^{1}) = 1\) 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 \({}^{8}\!\log(\frac{1}{8})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{8}\!\log(\frac{1}{8}) = {}^{8}\!\log(8^{-1}) = -1\) 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 \({}^{\frac{1}{7}}\!\log(49)\) Logaritme (6) 00fn - Rekenen met logaritmen - basis - 0ms b \({}^{\frac{1}{7}}\!\log({}^{\frac{1}{7}}\!\log(49)) = {}^{\frac{1}{7}}\!\log(\frac{1}{7}^{-2}) = -2\) 1p 1p c \({}^{7}\!\log(7 \sqrt{7})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{7}\!\log(7 \sqrt{7}) = {}^{7}\!\log(7^{1} ⋅ 7^{\frac{1}{2}}) = {}^{7}\!\log(7^{1\frac{1}{2}}) = 1\frac{1}{2}\) 1p 1p d \({}^{4}\!\log(4^{0{,}4})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{4}\!\log(4^{0{,}4}) = 0{,}4\) 1p |