Getal & Ruimte (13e editie) - vwo wiskunde B
'Logaritmen herleiden'.
| vwo wiskunde B | 9.2 Rekenregels voor logaritmen |
opgave 1Herleid tot één logaritme. 1p a \({}^{5}\!\log(2 x) + {}^{5}\!\log(3 x - 4)\) Optellen (1) 00ku - Logaritmen herleiden - basis - basis - 0ms - dynamic variables a \({}^{5}\!\log(2 x) + {}^{5}\!\log(3 x - 4)\) 1p 1p b \({}^{5}\!\log(2) - {}^{5}\!\log(a + 4)\) Aftrekken 00kv - Logaritmen herleiden - basis - eind - 1ms - dynamic variables b \({}^{5}\!\log(2) - {}^{5}\!\log(a + 4)\) 1p 2p c \(2 ⋅ {}^{4}\!\log(p + 5)\) Vermenigvuldigen 00kw - Logaritmen herleiden - basis - midden - 0ms - dynamic variables c \(2 ⋅ {}^{4}\!\log(p + 5)\) 1p ○ \(\text{ } = {}^{4}\!\log(p^{2} + 10 p + 25)\) 1p 2p d \(4 ⋅ {}^{3}\!\log(x) + {}^{3}\!\log(2 x - 5)\) OptellenVermenigvuldigen 00kx - Logaritmen herleiden - basis - eind - 0ms - dynamic variables d \(4 ⋅ {}^{3}\!\log(x) + {}^{3}\!\log(2 x - 5)\) 1p ○ \(\text{ } = {}^{3}\!\log(x^{4} ⋅ (2 x - 5))\) 1p opgave 2Herleid tot één logaritme. 2p a \(3 + {}^{4}\!\log(2 a + 5)\) Grondtal (1) 00ky - Logaritmen herleiden - basis - midden - 0ms - dynamic variables a \(3 + {}^{4}\!\log(2 a + 5)\) 1p ○ \(\text{ } = {}^{4}\!\log(64 ⋅ (2 a + 5))\) 1p 3p b \({}^{4}\!\log(1\,024) + {}^{3}\!\log(2 x - 1)\) Grondtal (2) 00kz - Logaritmen herleiden - basis - eind - 0ms - dynamic variables b \({}^{4}\!\log(1\,024) + {}^{3}\!\log(2 x - 1)\) 1p ○ \(\text{ } = {}^{3}\!\log(3^{5}) + {}^{3}\!\log(2 x - 1)\) 1p ○ \(\text{ } = {}^{3}\!\log(243 ⋅ (2 x - 1))\) 1p |