Getal & Ruimte (12e editie) - havo wiskunde B
'Rekenen met logaritmen'.
| havo wiskunde B | 5.5 Logaritmen |
opgave 1Bereken. 1p a \({}^{7}\!\log(49)\) Logaritme (1) 00fi - Rekenen met logaritmen - basis - 0ms a \({}^{7}\!\log(49) = {}^{7}\!\log(7^{2}) = 2\) 1p 1p b \({}^{6}\!\log(6)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 0ms b \({}^{6}\!\log(6) = {}^{6}\!\log(6^{1}) = 1\) 1p 1p c \(\log(10)\) Logaritme (3) 00fk - Rekenen met logaritmen - basis - 0ms c \(\log(10) = \log(10^{1}) = 1\) 1p 1p d \({}^{4}\!\log(\frac{1}{4})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{4}\!\log(\frac{1}{4}) = {}^{4}\!\log(4^{-1}) = -1\) 1p opgave 2Bereken. 1p a \({}^{\frac{1}{3}}\!\log(\frac{1}{9})\) Logaritme (5) 00fm - Rekenen met logaritmen - basis - 0ms a \({}^{\frac{1}{3}}\!\log(\frac{1}{9}) = {}^{\frac{1}{3}}\!\log(\frac{1}{3}^{2}) = 2\) 1p 1p b \({}^{\frac{1}{3}}\!\log(27)\) Logaritme (6) 00fn - Rekenen met logaritmen - basis - 0ms b \({}^{\frac{1}{3}}\!\log({}^{\frac{1}{3}}\!\log(27)) = {}^{\frac{1}{3}}\!\log(\frac{1}{3}^{-3}) = -3\) 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 \({}^{3}\!\log(3^{0{,}8})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{3}\!\log(3^{0{,}8}) = 0{,}8\) 1p |