Getal & Ruimte (12e editie) - vwo wiskunde B
'Logaritmen herleiden'.
| vwo wiskunde B | 9.1 Rekenregels voor logaritmen |
opgave 1Herleid tot één logaritme. 1p a \({}^{5}\!\log(4) + {}^{5}\!\log(a - 2)\) Optellen (1) 00ku - Logaritmen herleiden - basis - basis - 1ms - dynamic variables a \({}^{5}\!\log(4) + {}^{5}\!\log(a - 2)\) 1p 1p b \({}^{3}\!\log(x) - {}^{3}\!\log(2 x + 4)\) Aftrekken 00kv - Logaritmen herleiden - basis - eind - 1ms - dynamic variables b \({}^{3}\!\log(x) - {}^{3}\!\log(2 x + 4)\) 1p 2p c \(2 ⋅ {}^{3}\!\log(4 x)\) Vermenigvuldigen 00kw - Logaritmen herleiden - basis - midden - 1ms - dynamic variables c \(2 ⋅ {}^{3}\!\log(4 x)\) 1p ○ \(\text{ } = {}^{3}\!\log(16 x^{2})\) 1p 2p d \(5 ⋅ {}^{4}\!\log(p) + {}^{4}\!\log(3 p + 1)\) OptellenVermenigvuldigen 00kx - Logaritmen herleiden - basis - eind - 1ms - dynamic variables d \(5 ⋅ {}^{4}\!\log(p) + {}^{4}\!\log(3 p + 1)\) 1p ○ \(\text{ } = {}^{4}\!\log(p^{5} ⋅ (3 p + 1))\) 1p opgave 2Herleid tot één logaritme. 2p a \(2 + {}^{4}\!\log(3 a - 5)\) Grondtal (1) 00ky - Logaritmen herleiden - basis - midden - 1ms - dynamic variables a \(2 + {}^{4}\!\log(3 a - 5)\) 1p ○ \(\text{ } = {}^{4}\!\log(16 ⋅ (3 a - 5))\) 1p 3p b \({}^{2}\!\log(32) + {}^{4}\!\log(3 p - 1)\) Grondtal (2) 00kz - Logaritmen herleiden - basis - eind - 1ms - dynamic variables b \({}^{2}\!\log(32) + {}^{4}\!\log(3 p - 1)\) 1p ○ \(\text{ } = {}^{4}\!\log(4^{5}) + {}^{4}\!\log(3 p - 1)\) 1p ○ \(\text{ } = {}^{4}\!\log(1\,024 ⋅ (3 p - 1))\) 1p |