Getal & Ruimte (12e editie) - vwo wiskunde B
'Logaritmen herleiden'.
| vwo wiskunde B | 9.1 Rekenregels voor logaritmen |
opgave 1Herleid tot één logaritme. 1p a \({}^{5}\!\log(2) + {}^{5}\!\log(p - 4)\) Optellen (1) 00ku - Logaritmen herleiden - basis - basis - 0ms - dynamic variables a \({}^{5}\!\log(2) + {}^{5}\!\log(p - 4)\) 1p 1p b \({}^{3}\!\log(2) - {}^{3}\!\log(4 a - 1)\) Aftrekken 00kv - Logaritmen herleiden - basis - eind - 1ms - dynamic variables b \({}^{3}\!\log(2) - {}^{3}\!\log(4 a - 1)\) 1p 2p c \(5 ⋅ {}^{4}\!\log(2 x)\) Vermenigvuldigen 00kw - Logaritmen herleiden - basis - midden - 1ms - dynamic variables c \(5 ⋅ {}^{4}\!\log(2 x)\) 1p ○ \(\text{ } = {}^{4}\!\log(32 x^{5})\) 1p 2p d \(4 ⋅ {}^{5}\!\log(x) + {}^{5}\!\log(2 x - 1)\) OptellenVermenigvuldigen 00kx - Logaritmen herleiden - basis - eind - 0ms - dynamic variables d \(4 ⋅ {}^{5}\!\log(x) + {}^{5}\!\log(2 x - 1)\) 1p ○ \(\text{ } = {}^{5}\!\log(x^{4} ⋅ (2 x - 1))\) 1p opgave 2Herleid tot één logaritme. 2p a \(3 + {}^{5}\!\log(2 a + 4)\) Grondtal (1) 00ky - Logaritmen herleiden - basis - midden - 0ms - dynamic variables a \(3 + {}^{5}\!\log(2 a + 4)\) 1p ○ \(\text{ } = {}^{5}\!\log(125 ⋅ (2 a + 4))\) 1p 3p b \({}^{2}\!\log(8) + {}^{4}\!\log(5 p - 1)\) Grondtal (2) 00kz - Logaritmen herleiden - basis - eind - 0ms - dynamic variables b \({}^{2}\!\log(8) + {}^{4}\!\log(5 p - 1)\) 1p ○ \(\text{ } = {}^{4}\!\log(4^{3}) + {}^{4}\!\log(5 p - 1)\) 1p ○ \(\text{ } = {}^{4}\!\log(64 ⋅ (5 p - 1))\) 1p |