Getal & Ruimte (12e editie) - vwo wiskunde B
'Logaritmen herleiden'.
| vwo wiskunde B | 9.1 Rekenregels voor logaritmen |
opgave 1Herleid tot één logaritme. 1p a \({}^{4}\!\log(5) + {}^{4}\!\log(2 x - 3)\) Optellen (1) 00ku - Logaritmen herleiden - basis - basis - 0ms - dynamic variables a \({}^{4}\!\log(5) + {}^{4}\!\log(2 x - 3)\) 1p 1p b \({}^{2}\!\log(4 p) - {}^{2}\!\log(5 p + 3)\) Aftrekken 00kv - Logaritmen herleiden - basis - eind - 0ms - dynamic variables b \({}^{2}\!\log(4 p) - {}^{2}\!\log(5 p + 3)\) 1p 2p c \(3 ⋅ {}^{2}\!\log(5 a)\) Vermenigvuldigen 00kw - Logaritmen herleiden - basis - midden - 1ms - dynamic variables c \(3 ⋅ {}^{2}\!\log(5 a)\) 1p ○ \(\text{ } = {}^{2}\!\log(125 a^{3})\) 1p 2p d \(5 ⋅ {}^{2}\!\log(a) + {}^{2}\!\log(3 a - 1)\) OptellenVermenigvuldigen 00kx - Logaritmen herleiden - basis - eind - 0ms - dynamic variables d \(5 ⋅ {}^{2}\!\log(a) + {}^{2}\!\log(3 a - 1)\) 1p ○ \(\text{ } = {}^{2}\!\log(a^{5} ⋅ (3 a - 1))\) 1p opgave 2Herleid tot één logaritme. 2p a \(2 + {}^{3}\!\log(5 x - 4)\) Grondtal (1) 00ky - Logaritmen herleiden - basis - midden - 0ms - dynamic variables a \(2 + {}^{3}\!\log(5 x - 4)\) 1p ○ \(\text{ } = {}^{3}\!\log(9 ⋅ (5 x - 4))\) 1p 3p b \({}^{2}\!\log(8) + {}^{4}\!\log(a + 5)\) Grondtal (2) 00kz - Logaritmen herleiden - basis - eind - 0ms - dynamic variables b \({}^{2}\!\log(8) + {}^{4}\!\log(a + 5)\) 1p ○ \(\text{ } = {}^{4}\!\log(4^{3}) + {}^{4}\!\log(a + 5)\) 1p ○ \(\text{ } = {}^{4}\!\log(64 ⋅ (a + 5))\) 1p |