Getal & Ruimte (13e editie) - havo wiskunde B
'Rekenen met logaritmen'.
| havo wiskunde B | 5.5 Logaritmen |
opgave 1Bereken. 1p a \({}^{5}\!\log(25)\) Logaritme (1) 00fi - Rekenen met logaritmen - basis - 0ms a \({}^{5}\!\log(25) = {}^{5}\!\log(5^{2}) = 2\) 1p 1p b \({}^{9}\!\log(9)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 0ms b \({}^{9}\!\log(9) = {}^{9}\!\log(9^{1}) = 1\) 1p 1p c \({}^{4}\!\log(\frac{1}{4})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms c \({}^{4}\!\log(\frac{1}{4}) = {}^{4}\!\log(4^{-1}) = -1\) 1p 1p d \({}^{\frac{1}{4}}\!\log(\frac{1}{16})\) Logaritme (5) 00fm - Rekenen met logaritmen - basis - 0ms d \({}^{\frac{1}{4}}\!\log(\frac{1}{16}) = {}^{\frac{1}{4}}\!\log(\frac{1}{4}^{2}) = 2\) 1p opgave 2Bereken. 1p a \({}^{\frac{1}{5}}\!\log(25)\) Logaritme (6) 00fn - Rekenen met logaritmen - basis - 0ms a \({}^{\frac{1}{5}}\!\log({}^{\frac{1}{5}}\!\log(25)) = {}^{\frac{1}{5}}\!\log(\frac{1}{5}^{-2}) = -2\) 1p 1p b \({}^{5}\!\log(5 \sqrt{5})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms b \({}^{5}\!\log(5 \sqrt{5}) = {}^{5}\!\log(5^{1} ⋅ 5^{\frac{1}{2}}) = {}^{5}\!\log(5^{1\frac{1}{2}}) = 1\frac{1}{2}\) 1p 1p c \({}^{2}\!\log(2^{0{,}7})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms c \({}^{2}\!\log(2^{0{,}7}) = 0{,}7\) 1p |