Getal & Ruimte (12e editie) - vwo wiskunde B
'Rekenen met logaritmen'.
| vwo wiskunde B | 5.4 Logaritmen |
opgave 1Bereken. 1p a \({}^{2}\!\log(4)\) Logaritme (1) 00fi - Rekenen met logaritmen - basis - 0ms a \({}^{2}\!\log(4)={}^{2}\!\log(2^2)=2\) 1p 1p b \({}^{7}\!\log(7)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 0ms b \({}^{7}\!\log(7)={}^{7}\!\log(7^1)=1\) 1p 1p c \(\log(1\,000\,000)\) Logaritme (3) 00fk - Rekenen met logaritmen - basis - 0ms c \(\log(1\,000\,000)=\log(10^6)=6\) 1p 1p d \({}^{7}\!\log(\frac{1}{49})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{7}\!\log(\frac{1}{49})={}^{7}\!\log(7^{-2})=-2\) 1p opgave 2Bereken. 1p a \({}^{\frac{1}{8}}\!\log(\frac{1}{64})\) Logaritme (5) 00fm - Rekenen met logaritmen - basis - 1ms a \({}^{\frac{1}{8}}\!\log(\frac{1}{64})={}^{\frac{1}{8}}\!\log(\frac{1}{8}^2)=2\) 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 \({}^{2}\!\log(2\sqrt{2})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{2}\!\log(2\sqrt{2})={}^{2}\!\log(2^1⋅2^{\frac{1}{2}})={}^{2}\!\log(2^{1\frac{1}{2}})=1\frac{1}{2}\) 1p 1p d \({}^{3}\!\log(3^{8{,}8})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{3}\!\log(3^{8{,}8})=8{,}8\) 1p |