Getal & Ruimte (12e editie) - havo wiskunde B
'Logaritmen herleiden'.
| havo wiskunde B | 9.3 Rekenregels voor logaritmen |
opgave 1Herleid tot één logaritme. 1p a \({}^{5}\!\log(3 p) + {}^{5}\!\log(p + 2)\) Optellen (1) 00ku - Logaritmen herleiden - basis - basis - 0ms - dynamic variables a \({}^{5}\!\log(3 p) + {}^{5}\!\log(p + 2)\) 1p 1p b \({}^{3}\!\log(2 x) - {}^{3}\!\log(x - 5)\) Aftrekken 00kv - Logaritmen herleiden - basis - eind - 1ms - dynamic variables b \({}^{3}\!\log(2 x) - {}^{3}\!\log(x - 5)\) 1p 2p c \(2 ⋅ {}^{4}\!\log(a + 3)\) Vermenigvuldigen 00kw - Logaritmen herleiden - basis - midden - 0ms - dynamic variables c \(2 ⋅ {}^{4}\!\log(a + 3)\) 1p ○ \(\text{ } = {}^{4}\!\log(a^{2} + 6 a + 9)\) 1p 2p d \(3 ⋅ {}^{5}\!\log(a) + {}^{5}\!\log(2 a - 4)\) OptellenVermenigvuldigen 00kx - Logaritmen herleiden - basis - eind - 0ms - dynamic variables d \(3 ⋅ {}^{5}\!\log(a) + {}^{5}\!\log(2 a - 4)\) 1p ○ \(\text{ } = {}^{5}\!\log(a^{3} ⋅ (2 a - 4))\) 1p opgave 2Herleid tot één logaritme. 2p a \(4 + {}^{3}\!\log(x - 5)\) Grondtal (1) 00ky - Logaritmen herleiden - basis - midden - 0ms - dynamic variables a \(4 + {}^{3}\!\log(x - 5)\) 1p ○ \(\text{ } = {}^{3}\!\log(81 ⋅ (x - 5))\) 1p 3p b \({}^{4}\!\log(1\,024) + {}^{3}\!\log(x - 2)\) Grondtal (2) 00kz - Logaritmen herleiden - basis - eind - 0ms - dynamic variables b \({}^{4}\!\log(1\,024) + {}^{3}\!\log(x - 2)\) 1p ○ \(\text{ } = {}^{3}\!\log(3^{5}) + {}^{3}\!\log(x - 2)\) 1p ○ \(\text{ } = {}^{3}\!\log(243 ⋅ (x - 2))\) 1p |