Getal & Ruimte (12e editie) - vwo wiskunde B
'Logaritmen herleiden'.
| vwo wiskunde B | 9.1 Rekenregels voor logaritmen |
opgave 1Herleid tot één logaritme. 1p a \({}^{3}\!\log(5 a) + {}^{3}\!\log(4 a + 2)\) Optellen (1) 00ku - Logaritmen herleiden - basis - basis - 0ms - dynamic variables a \({}^{3}\!\log(5 a) + {}^{3}\!\log(4 a + 2)\) 1p 1p b \({}^{5}\!\log(2 p) - {}^{5}\!\log(3 p - 4)\) Aftrekken 00kv - Logaritmen herleiden - basis - eind - 0ms - dynamic variables b \({}^{5}\!\log(2 p) - {}^{5}\!\log(3 p - 4)\) 1p 2p c \(3 ⋅ {}^{5}\!\log(2 a)\) Vermenigvuldigen 00kw - Logaritmen herleiden - basis - midden - 1ms - dynamic variables c \(3 ⋅ {}^{5}\!\log(2 a)\) 1p ○ \(\text{ } = {}^{5}\!\log(8 a^{3})\) 1p 2p d \(4 ⋅ {}^{2}\!\log(x) + {}^{2}\!\log(5 x + 3)\) OptellenVermenigvuldigen 00kx - Logaritmen herleiden - basis - eind - 0ms - dynamic variables d \(4 ⋅ {}^{2}\!\log(x) + {}^{2}\!\log(5 x + 3)\) 1p ○ \(\text{ } = {}^{2}\!\log(x^{4} ⋅ (5 x + 3))\) 1p opgave 2Herleid tot één logaritme. 2p a \(2 + {}^{3}\!\log(4 x - 5)\) Grondtal (1) 00ky - Logaritmen herleiden - basis - midden - 0ms - dynamic variables a \(2 + {}^{3}\!\log(4 x - 5)\) 1p ○ \(\text{ } = {}^{3}\!\log(9 ⋅ (4 x - 5))\) 1p 3p b \({}^{5}\!\log(25) + {}^{4}\!\log(a - 3)\) Grondtal (2) 00kz - Logaritmen herleiden - basis - eind - 0ms - dynamic variables b \({}^{5}\!\log(25) + {}^{4}\!\log(a - 3)\) 1p ○ \(\text{ } = {}^{4}\!\log(4^{2}) + {}^{4}\!\log(a - 3)\) 1p ○ \(\text{ } = {}^{4}\!\log(16 ⋅ (a - 3))\) 1p |