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 \({}^{7}\!\log(1)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 0ms b \({}^{7}\!\log(1) = {}^{7}\!\log(7^{0}) = 0\) 1p 1p c \(\log(10\,000)\) Logaritme (3) 00fk - Rekenen met logaritmen - basis - 0ms c \(\log(10\,000) = \log(10^{4}) = 4\) 1p 1p d \({}^{2}\!\log(\frac{1}{2})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{2}\!\log(\frac{1}{2}) = {}^{2}\!\log(2^{-1}) = -1\) 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 \({}^{\frac{1}{10}}\!\log(100)\) Logaritme (6) 00fn - Rekenen met logaritmen - basis - 0ms b \({}^{\frac{1}{10}}\!\log({}^{\frac{1}{10}}\!\log(100)) = {}^{\frac{1}{10}}\!\log(\frac{1}{10}^{-2}) = -2\) 1p 1p c \({}^{4}\!\log(16 \sqrt{4})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{4}\!\log(16 \sqrt{4}) = {}^{4}\!\log(4^{2} ⋅ 4^{\frac{1}{2}}) = {}^{4}\!\log(4^{2\frac{1}{2}}) = 2\frac{1}{2}\) 1p 1p d \({}^{4}\!\log(4^{3{,}5})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{4}\!\log(4^{3{,}5}) = 3{,}5\) 1p |