Getal & Ruimte (13e editie) - havo wiskunde B
'Logaritmen herleiden'.
| havo wiskunde B | 9.3 Rekenregels voor logaritmen |
opgave 1Herleid tot één logaritme. 1p a \({}^{5}\!\log(3) + {}^{5}\!\log(2 a + 4)\) Optellen (1) 00ku - Logaritmen herleiden - basis - basis - 0ms - dynamic variables a \({}^{5}\!\log(3) + {}^{5}\!\log(2 a + 4)\) 1p 1p b \({}^{2}\!\log(5 x) - {}^{2}\!\log(x - 3)\) Aftrekken 00kv - Logaritmen herleiden - basis - eind - 0ms - dynamic variables b \({}^{2}\!\log(5 x) - {}^{2}\!\log(x - 3)\) 1p 2p c \(5 ⋅ {}^{2}\!\log(4 a)\) Vermenigvuldigen 00kw - Logaritmen herleiden - basis - midden - 1ms - dynamic variables c \(5 ⋅ {}^{2}\!\log(4 a)\) 1p ○ \(\text{ } = {}^{2}\!\log(1\,024 a^{5})\) 1p 2p d \(2 ⋅ {}^{3}\!\log(x) + {}^{3}\!\log(5 x + 4)\) OptellenVermenigvuldigen 00kx - Logaritmen herleiden - basis - eind - 0ms - dynamic variables d \(2 ⋅ {}^{3}\!\log(x) + {}^{3}\!\log(5 x + 4)\) 1p ○ \(\text{ } = {}^{3}\!\log(x^{2} ⋅ (5 x + 4))\) 1p opgave 2Herleid tot één logaritme. 2p a \(3 + {}^{2}\!\log(4 p - 1)\) Grondtal (1) 00ky - Logaritmen herleiden - basis - midden - 0ms - dynamic variables a \(3 + {}^{2}\!\log(4 p - 1)\) 1p ○ \(\text{ } = {}^{2}\!\log(8 ⋅ (4 p - 1))\) 1p 3p b \({}^{3}\!\log(9) + {}^{5}\!\log(4 a + 1)\) Grondtal (2) 00kz - Logaritmen herleiden - basis - eind - 0ms - dynamic variables b \({}^{3}\!\log(9) + {}^{5}\!\log(4 a + 1)\) 1p ○ \(\text{ } = {}^{5}\!\log(5^{2}) + {}^{5}\!\log(4 a + 1)\) 1p ○ \(\text{ } = {}^{5}\!\log(25 ⋅ (4 a + 1))\) 1p |