Getal & Ruimte (12e editie) - vwo wiskunde B
'Logaritmen herleiden'.
| vwo wiskunde B | 9.1 Rekenregels voor logaritmen |
opgave 1Herleid tot één logaritme. 1p a \({}^{3}\!\log(4) + {}^{3}\!\log(5 x + 2)\) Optellen (1) 00ku - Logaritmen herleiden - basis - basis - 1ms - dynamic variables a \({}^{3}\!\log(4) + {}^{3}\!\log(5 x + 2)\) 1p 1p b \({}^{5}\!\log(2 a) - {}^{5}\!\log(a + 4)\) Aftrekken 00kv - Logaritmen herleiden - basis - eind - 1ms - dynamic variables b \({}^{5}\!\log(2 a) - {}^{5}\!\log(a + 4)\) 1p 2p c \(3 ⋅ {}^{4}\!\log(2 x)\) Vermenigvuldigen 00kw - Logaritmen herleiden - basis - midden - 1ms - dynamic variables c \(3 ⋅ {}^{4}\!\log(2 x)\) 1p ○ \(\text{ } = {}^{4}\!\log(8 x^{3})\) 1p 2p d \(5 ⋅ {}^{3}\!\log(p) + {}^{3}\!\log(4 p - 1)\) OptellenVermenigvuldigen 00kx - Logaritmen herleiden - basis - eind - 1ms - dynamic variables d \(5 ⋅ {}^{3}\!\log(p) + {}^{3}\!\log(4 p - 1)\) 1p ○ \(\text{ } = {}^{3}\!\log(p^{5} ⋅ (4 p - 1))\) 1p opgave 2Herleid tot één logaritme. 2p a \(4 + {}^{2}\!\log(a + 3)\) Grondtal (1) 00ky - Logaritmen herleiden - basis - midden - 1ms - dynamic variables a \(4 + {}^{2}\!\log(a + 3)\) 1p ○ \(\text{ } = {}^{2}\!\log(16 ⋅ (a + 3))\) 1p 3p b \({}^{5}\!\log(625) + {}^{3}\!\log(x - 2)\) Grondtal (2) 00kz - Logaritmen herleiden - basis - eind - 1ms - dynamic variables b \({}^{5}\!\log(625) + {}^{3}\!\log(x - 2)\) 1p ○ \(\text{ } = {}^{3}\!\log(3^{4}) + {}^{3}\!\log(x - 2)\) 1p ○ \(\text{ } = {}^{3}\!\log(81 ⋅ (x - 2))\) 1p |