Getal & Ruimte (13e editie) - havo wiskunde B
'Logaritmen herleiden'.
| havo wiskunde B | 9.3 Rekenregels voor logaritmen |
opgave 1Herleid tot één logaritme. 1p a \({}^{5}\!\log(a) + {}^{5}\!\log(4 a + 2)\) Optellen (1) 00ku - Logaritmen herleiden - basis - basis - 0ms - dynamic variables a \({}^{5}\!\log(a) + {}^{5}\!\log(4 a + 2)\) 1p 1p b \({}^{5}\!\log(2 p) - {}^{5}\!\log(4 p - 1)\) Aftrekken 00kv - Logaritmen herleiden - basis - eind - 0ms - dynamic variables b \({}^{5}\!\log(2 p) - {}^{5}\!\log(4 p - 1)\) 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 \(2 ⋅ {}^{3}\!\log(x) + {}^{3}\!\log(4 x - 5)\) OptellenVermenigvuldigen 00kx - Logaritmen herleiden - basis - eind - 0ms - dynamic variables d \(2 ⋅ {}^{3}\!\log(x) + {}^{3}\!\log(4 x - 5)\) 1p ○ \(\text{ } = {}^{3}\!\log(x^{2} ⋅ (4 x - 5))\) 1p opgave 2Herleid tot één logaritme. 2p a \(4 + {}^{3}\!\log(2 x - 5)\) Grondtal (1) 00ky - Logaritmen herleiden - basis - midden - 0ms - dynamic variables a \(4 + {}^{3}\!\log(2 x - 5)\) 1p ○ \(\text{ } = {}^{3}\!\log(81 ⋅ (2 x - 5))\) 1p 3p b \({}^{2}\!\log(16) + {}^{3}\!\log(5 x + 1)\) Grondtal (2) 00kz - Logaritmen herleiden - basis - eind - 0ms - dynamic variables b \({}^{2}\!\log(16) + {}^{3}\!\log(5 x + 1)\) 1p ○ \(\text{ } = {}^{3}\!\log(3^{4}) + {}^{3}\!\log(5 x + 1)\) 1p ○ \(\text{ } = {}^{3}\!\log(81 ⋅ (5 x + 1))\) 1p |