Getal & Ruimte (12e editie) - vwo wiskunde B
'Logaritmen herleiden'.
| vwo wiskunde B | 9.1 Rekenregels voor logaritmen |
opgave 1Herleid tot één logaritme. 1p a \({}^{4}\!\log(3) + {}^{4}\!\log(2 x + 5)\) Optellen (1) 00ku - Logaritmen herleiden - basis - basis - 0ms - dynamic variables a \({}^{4}\!\log(3) + {}^{4}\!\log(2 x + 5)\) 1p 1p b \({}^{2}\!\log(4) - {}^{2}\!\log(x + 5)\) Aftrekken 00kv - Logaritmen herleiden - basis - eind - 1ms - dynamic variables b \({}^{2}\!\log(4) - {}^{2}\!\log(x + 5)\) 1p 2p c \(3 ⋅ {}^{4}\!\log(5 a)\) Vermenigvuldigen 00kw - Logaritmen herleiden - basis - midden - 1ms - dynamic variables c \(3 ⋅ {}^{4}\!\log(5 a)\) 1p ○ \(\text{ } = {}^{4}\!\log(125 a^{3})\) 1p 2p d \(2 ⋅ {}^{3}\!\log(a) + {}^{3}\!\log(5 a - 4)\) OptellenVermenigvuldigen 00kx - Logaritmen herleiden - basis - eind - 0ms - dynamic variables d \(2 ⋅ {}^{3}\!\log(a) + {}^{3}\!\log(5 a - 4)\) 1p ○ \(\text{ } = {}^{3}\!\log(a^{2} ⋅ (5 a - 4))\) 1p opgave 2Herleid tot één logaritme. 2p a \(3 + {}^{5}\!\log(2 p + 1)\) Grondtal (1) 00ky - Logaritmen herleiden - basis - midden - 0ms - dynamic variables a \(3 + {}^{5}\!\log(2 p + 1)\) 1p ○ \(\text{ } = {}^{5}\!\log(125 ⋅ (2 p + 1))\) 1p 3p b \({}^{3}\!\log(81) + {}^{2}\!\log(5 x + 1)\) Grondtal (2) 00kz - Logaritmen herleiden - basis - eind - 0ms - dynamic variables b \({}^{3}\!\log(81) + {}^{2}\!\log(5 x + 1)\) 1p ○ \(\text{ } = {}^{2}\!\log(2^{4}) + {}^{2}\!\log(5 x + 1)\) 1p ○ \(\text{ } = {}^{2}\!\log(16 ⋅ (5 x + 1))\) 1p |