Getal & Ruimte (12e editie) - havo wiskunde B
'Logaritmen herleiden'.
| havo wiskunde B | 9.3 Rekenregels voor logaritmen |
opgave 1Herleid tot één logaritme. 1p a \({}^{3}\!\log(2) + {}^{3}\!\log(p + 5)\) Optellen (1) 00ku - Logaritmen herleiden - basis - basis - 0ms - dynamic variables a \({}^{3}\!\log(2) + {}^{3}\!\log(p + 5)\) 1p 1p b \({}^{4}\!\log(5 x) - {}^{4}\!\log(2 x - 1)\) Aftrekken 00kv - Logaritmen herleiden - basis - eind - 1ms - dynamic variables b \({}^{4}\!\log(5 x) - {}^{4}\!\log(2 x - 1)\) 1p 2p c \(2 ⋅ {}^{3}\!\log(5 a)\) Vermenigvuldigen 00kw - Logaritmen herleiden - basis - midden - 0ms - dynamic variables c \(2 ⋅ {}^{3}\!\log(5 a)\) 1p ○ \(\text{ } = {}^{3}\!\log(25 a^{2})\) 1p 2p d \(5 ⋅ {}^{2}\!\log(a) + {}^{2}\!\log(3 a - 1)\) OptellenVermenigvuldigen 00kx - Logaritmen herleiden - basis - eind - 0ms - dynamic variables d \(5 ⋅ {}^{2}\!\log(a) + {}^{2}\!\log(3 a - 1)\) 1p ○ \(\text{ } = {}^{2}\!\log(a^{5} ⋅ (3 a - 1))\) 1p opgave 2Herleid tot één logaritme. 2p a \(4 + {}^{2}\!\log(3 x - 5)\) Grondtal (1) 00ky - Logaritmen herleiden - basis - midden - 0ms - dynamic variables a \(4 + {}^{2}\!\log(3 x - 5)\) 1p ○ \(\text{ } = {}^{2}\!\log(16 ⋅ (3 x - 5))\) 1p 3p b \({}^{4}\!\log(64) + {}^{2}\!\log(5 a - 1)\) Grondtal (2) 00kz - Logaritmen herleiden - basis - eind - 0ms - dynamic variables b \({}^{4}\!\log(64) + {}^{2}\!\log(5 a - 1)\) 1p ○ \(\text{ } = {}^{2}\!\log(2^{3}) + {}^{2}\!\log(5 a - 1)\) 1p ○ \(\text{ } = {}^{2}\!\log(8 ⋅ (5 a - 1))\) 1p |