Getal & Ruimte (12e editie) - vwo wiskunde A
'Rekenen met logaritmen'.
| vwo wiskunde A | 10.3 Logaritmen |
opgave 1Bereken. 1p a \({}^{8}\!\log(64)\) Logaritme (1) 00fi - Rekenen met logaritmen - basis a \({}^{8}\!\log(64)={}^{8}\!\log(8^2)=2\) 1p 1p b \({}^{6}\!\log(6)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis b \({}^{6}\!\log(6)={}^{6}\!\log(6^1)=1\) 1p 1p c \(\log(1\,000\,000)\) Logaritme (3) 00fk - Rekenen met logaritmen - basis c \(\log(1\,000\,000)=\log(10^6)=6\) 1p 1p d \({}^{9}\!\log(\frac{1}{81})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis d \({}^{9}\!\log(\frac{1}{81})={}^{9}\!\log(9^{-2})=-2\) 1p opgave 2Bereken. 1p a \({}^{\frac{1}{4}}\!\log(\frac{1}{16})\) Logaritme (5) 00fm - Rekenen met logaritmen - basis a \({}^{\frac{1}{4}}\!\log(\frac{1}{16})={}^{\frac{1}{4}}\!\log(\frac{1}{4}^2)=2\) 1p 1p b \({}^{\frac{1}{5}}\!\log(25)\) Logaritme (6) 00fn - Rekenen met logaritmen - basis b \({}^{\frac{1}{5}}\!\log({}^{\frac{1}{5}}\!\log(25))={}^{\frac{1}{5}}\!\log(\frac{1}{5}^{-2})=-2\) 1p 1p c \({}^{5}\!\log(125\sqrt{5})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis c \({}^{5}\!\log(125\sqrt{5})={}^{5}\!\log(5^3⋅5^{\frac{1}{2}})={}^{5}\!\log(5^{3\frac{1}{2}})=3\frac{1}{2}\) 1p 1p d \({}^{3}\!\log(3^{6{,}4})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis d \({}^{3}\!\log(3^{6{,}4})=6{,}4\) 1p |