Getal & Ruimte (12e editie) - vwo wiskunde A
'Rekenen met logaritmen'.
| vwo wiskunde A | 10.3 Logaritmen |
opgave 1Bereken. 1p a \({}^{4}\!\log(16)\) Logaritme (1) 00fi - Rekenen met logaritmen - basis - 0ms a \({}^{4}\!\log(16) = {}^{4}\!\log(4^{2}) = 2\) 1p 1p b \({}^{3}\!\log(3)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 0ms b \({}^{3}\!\log(3) = {}^{3}\!\log(3^{1}) = 1\) 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 \({}^{6}\!\log(\frac{1}{6})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{6}\!\log(\frac{1}{6}) = {}^{6}\!\log(6^{-1}) = -1\) 1p opgave 2Bereken. 1p a \({}^{\frac{1}{3}}\!\log(\frac{1}{27})\) Logaritme (5) 00fm - Rekenen met logaritmen - basis - 0ms a \({}^{\frac{1}{3}}\!\log(\frac{1}{27}) = {}^{\frac{1}{3}}\!\log(\frac{1}{3}^{3}) = 3\) 1p 1p b \({}^{\frac{1}{4}}\!\log(16)\) Logaritme (6) 00fn - Rekenen met logaritmen - basis - 0ms b \({}^{\frac{1}{4}}\!\log({}^{\frac{1}{4}}\!\log(16)) = {}^{\frac{1}{4}}\!\log(\frac{1}{4}^{-2}) = -2\) 1p 1p c \({}^{4}\!\log(64 \sqrt{4})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{4}\!\log(64 \sqrt{4}) = {}^{4}\!\log(4^{3} ⋅ 4^{\frac{1}{2}}) = {}^{4}\!\log(4^{3\frac{1}{2}}) = 3\frac{1}{2}\) 1p 1p d \({}^{7}\!\log(7^{3{,}3})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{7}\!\log(7^{3{,}3}) = 3{,}3\) 1p |