Getal & Ruimte (12e editie) - vwo wiskunde B
'Logaritmen herleiden'.
| vwo wiskunde B | 9.1 Rekenregels voor logaritmen |
opgave 1Herleid tot één logaritme. 1p a \({}^{5}\!\log(4) + {}^{5}\!\log(3 a + 2)\) Optellen (1) 00ku - Logaritmen herleiden - basis - basis - 1ms - dynamic variables a \({}^{5}\!\log(4) + {}^{5}\!\log(3 a + 2)\) 1p 1p b \({}^{3}\!\log(4 x) - {}^{3}\!\log(x - 2)\) Aftrekken 00kv - Logaritmen herleiden - basis - eind - 1ms - dynamic variables b \({}^{3}\!\log(4 x) - {}^{3}\!\log(x - 2)\) 1p 2p c \(5 ⋅ {}^{2}\!\log(4 x)\) Vermenigvuldigen 00kw - Logaritmen herleiden - basis - midden - 1ms - dynamic variables c \(5 ⋅ {}^{2}\!\log(4 x)\) 1p ○ \(\text{ } = {}^{2}\!\log(1\,024 x^{5})\) 1p 2p d \(2 ⋅ {}^{4}\!\log(p) + {}^{4}\!\log(5 p - 3)\) OptellenVermenigvuldigen 00kx - Logaritmen herleiden - basis - eind - 1ms - dynamic variables d \(2 ⋅ {}^{4}\!\log(p) + {}^{4}\!\log(5 p - 3)\) 1p ○ \(\text{ } = {}^{4}\!\log(p^{2} ⋅ (5 p - 3))\) 1p opgave 2Herleid tot één logaritme. 2p a \(2 + {}^{3}\!\log(5 a - 4)\) Grondtal (1) 00ky - Logaritmen herleiden - basis - midden - 1ms - dynamic variables a \(2 + {}^{3}\!\log(5 a - 4)\) 1p ○ \(\text{ } = {}^{3}\!\log(9 ⋅ (5 a - 4))\) 1p 3p b \({}^{5}\!\log(625) + {}^{3}\!\log(2 x + 1)\) Grondtal (2) 00kz - Logaritmen herleiden - basis - eind - 1ms - dynamic variables b \({}^{5}\!\log(625) + {}^{3}\!\log(2 x + 1)\) 1p ○ \(\text{ } = {}^{3}\!\log(3^{4}) + {}^{3}\!\log(2 x + 1)\) 1p ○ \(\text{ } = {}^{3}\!\log(81 ⋅ (2 x + 1))\) 1p |