Getal & Ruimte (12e editie) - vwo wiskunde B
'Logaritmen herleiden'.
| vwo wiskunde B | 9.1 Rekenregels voor logaritmen |
opgave 1Herleid tot één logaritme. 1p a \({}^{2}\!\log(p) + {}^{2}\!\log(4 p + 3)\) Optellen (1) 00ku - Logaritmen herleiden - basis - basis - 0ms - dynamic variables a \({}^{2}\!\log(p) + {}^{2}\!\log(4 p + 3)\) 1p 1p b \({}^{2}\!\log(3 a) - {}^{2}\!\log(4 a - 5)\) Aftrekken 00kv - Logaritmen herleiden - basis - eind - 1ms - dynamic variables b \({}^{2}\!\log(3 a) - {}^{2}\!\log(4 a - 5)\) 1p 2p c \(2 ⋅ {}^{3}\!\log(a + 5)\) Vermenigvuldigen 00kw - Logaritmen herleiden - basis - midden - 0ms - dynamic variables c \(2 ⋅ {}^{3}\!\log(a + 5)\) 1p ○ \(\text{ } = {}^{3}\!\log(a^{2} + 10 a + 25)\) 1p 2p d \(2 ⋅ {}^{4}\!\log(x) + {}^{4}\!\log(3 x - 1)\) OptellenVermenigvuldigen 00kx - Logaritmen herleiden - basis - eind - 0ms - dynamic variables d \(2 ⋅ {}^{4}\!\log(x) + {}^{4}\!\log(3 x - 1)\) 1p ○ \(\text{ } = {}^{4}\!\log(x^{2} ⋅ (3 x - 1))\) 1p opgave 2Herleid tot één logaritme. 2p a \(3 + {}^{5}\!\log(4 x - 2)\) Grondtal (1) 00ky - Logaritmen herleiden - basis - midden - 0ms - dynamic variables a \(3 + {}^{5}\!\log(4 x - 2)\) 1p ○ \(\text{ } = {}^{5}\!\log(125 ⋅ (4 x - 2))\) 1p 3p b \({}^{4}\!\log(1\,024) + {}^{2}\!\log(x + 3)\) Grondtal (2) 00kz - Logaritmen herleiden - basis - eind - 0ms - dynamic variables b \({}^{4}\!\log(1\,024) + {}^{2}\!\log(x + 3)\) 1p ○ \(\text{ } = {}^{2}\!\log(2^{5}) + {}^{2}\!\log(x + 3)\) 1p ○ \(\text{ } = {}^{2}\!\log(32 ⋅ (x + 3))\) 1p |