Getal & Ruimte (13e editie) - havo wiskunde B
'Logaritmen herleiden'.
| havo wiskunde B | 9.3 Rekenregels voor logaritmen |
opgave 1Herleid tot één logaritme. 1p a \({}^{4}\!\log(2) + {}^{4}\!\log(a + 5)\) Optellen (1) 00ku - Logaritmen herleiden - basis - basis - 0ms - dynamic variables a \({}^{4}\!\log(2) + {}^{4}\!\log(a + 5)\) 1p 1p b \({}^{5}\!\log(4 x) - {}^{5}\!\log(3 x - 2)\) Aftrekken 00kv - Logaritmen herleiden - basis - eind - 1ms - dynamic variables b \({}^{5}\!\log(4 x) - {}^{5}\!\log(3 x - 2)\) 1p 2p c \(3 ⋅ {}^{4}\!\log(5 a)\) Vermenigvuldigen 00kw - Logaritmen herleiden - basis - midden - 0ms - dynamic variables c \(3 ⋅ {}^{4}\!\log(5 a)\) 1p ○ \(\text{ } = {}^{4}\!\log(125 a^{3})\) 1p 2p d \(2 ⋅ {}^{4}\!\log(p) + {}^{4}\!\log(5 p + 3)\) OptellenVermenigvuldigen 00kx - Logaritmen herleiden - basis - eind - 0ms - 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 \(2 + {}^{3}\!\log(5 x + 4)\) 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 \({}^{3}\!\log(9) + {}^{5}\!\log(4 p - 1)\) Grondtal (2) 00kz - Logaritmen herleiden - basis - eind - 0ms - dynamic variables b \({}^{3}\!\log(9) + {}^{5}\!\log(4 p - 1)\) 1p ○ \(\text{ } = {}^{5}\!\log(5^{2}) + {}^{5}\!\log(4 p - 1)\) 1p ○ \(\text{ } = {}^{5}\!\log(25 ⋅ (4 p - 1))\) 1p |