Getal & Ruimte (12e editie) - havo wiskunde B
'Logaritmen herleiden'.
| havo wiskunde B | 9.3 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 \({}^{4}\!\log(2 p) - {}^{4}\!\log(5 p + 3)\) Aftrekken 00kv - Logaritmen herleiden - basis - eind - 0ms - dynamic variables b \({}^{4}\!\log(2 p) - {}^{4}\!\log(5 p + 3)\) 1p 2p c \(2 ⋅ {}^{5}\!\log(4 x)\) Vermenigvuldigen 00kw - Logaritmen herleiden - basis - midden - 1ms - dynamic variables c \(2 ⋅ {}^{5}\!\log(4 x)\) 1p ○ \(\text{ } = {}^{5}\!\log(16 x^{2})\) 1p 2p d \(4 ⋅ {}^{2}\!\log(a) + {}^{2}\!\log(5 a + 1)\) OptellenVermenigvuldigen 00kx - Logaritmen herleiden - basis - eind - 0ms - dynamic variables d \(4 ⋅ {}^{2}\!\log(a) + {}^{2}\!\log(5 a + 1)\) 1p ○ \(\text{ } = {}^{2}\!\log(a^{4} ⋅ (5 a + 1))\) 1p opgave 2Herleid tot één logaritme. 2p a \(3 + {}^{5}\!\log(4 a + 2)\) Grondtal (1) 00ky - Logaritmen herleiden - basis - midden - 0ms - dynamic variables a \(3 + {}^{5}\!\log(4 a + 2)\) 1p ○ \(\text{ } = {}^{5}\!\log(125 ⋅ (4 a + 2))\) 1p 3p b \({}^{3}\!\log(81) + {}^{5}\!\log(2 a - 1)\) Grondtal (2) 00kz - Logaritmen herleiden - basis - eind - 0ms - dynamic variables b \({}^{3}\!\log(81) + {}^{5}\!\log(2 a - 1)\) 1p ○ \(\text{ } = {}^{5}\!\log(5^{4}) + {}^{5}\!\log(2 a - 1)\) 1p ○ \(\text{ } = {}^{5}\!\log(625 ⋅ (2 a - 1))\) 1p |