Getal & Ruimte (13e editie) - vwo wiskunde B
'Rekenen met logaritmen'.
| vwo wiskunde B | 5.5 Logaritmen |
opgave 1Bereken. 1p a \({}^{2}\!\log(8)\) Logaritme (1) 00fi - Rekenen met logaritmen - basis - 0ms a \({}^{2}\!\log(8) = {}^{2}\!\log(2^{3}) = 3\) 1p 1p b \({}^{4}\!\log(1)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 0ms b \({}^{4}\!\log(1) = {}^{4}\!\log(4^{0}) = 0\) 1p 1p c \(\log(10)\) Logaritme (3) 00fk - Rekenen met logaritmen - basis - 0ms c \(\log(10) = \log(10^{1}) = 1\) 1p 1p d \({}^{2}\!\log(\frac{1}{16})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{2}\!\log(\frac{1}{16}) = {}^{2}\!\log(2^{-4}) = -4\) 1p opgave 2Bereken. 1p a \({}^{\frac{1}{6}}\!\log(\frac{1}{36})\) Logaritme (5) 00fm - Rekenen met logaritmen - basis - 0ms a \({}^{\frac{1}{6}}\!\log(\frac{1}{36}) = {}^{\frac{1}{6}}\!\log(\frac{1}{6}^{2}) = 2\) 1p 1p b \({}^{\frac{1}{5}}\!\log(125)\) Logaritme (6) 00fn - Rekenen met logaritmen - basis - 0ms b \({}^{\frac{1}{5}}\!\log({}^{\frac{1}{5}}\!\log(125)) = {}^{\frac{1}{5}}\!\log(\frac{1}{5}^{-3}) = -3\) 1p 1p c \({}^{7}\!\log(49 \sqrt{7})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{7}\!\log(49 \sqrt{7}) = {}^{7}\!\log(7^{2} ⋅ 7^{\frac{1}{2}}) = {}^{7}\!\log(7^{2\frac{1}{2}}) = 2\frac{1}{2}\) 1p 1p d \({}^{2}\!\log(2^{6{,}1})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{2}\!\log(2^{6{,}1}) = 6{,}1\) 1p |