Getal & Ruimte (13e editie) - vwo wiskunde B
'Logaritmen herleiden'.
| vwo wiskunde B | 9.2 Rekenregels voor logaritmen |
opgave 1Herleid tot één logaritme. 1p a \({}^{2}\!\log(5) + {}^{2}\!\log(3 a - 4)\) Optellen (1) 00ku - Logaritmen herleiden - basis - basis - 0ms - dynamic variables a \({}^{2}\!\log(5) + {}^{2}\!\log(3 a - 4)\) 1p 1p b \({}^{2}\!\log(x) - {}^{2}\!\log(5 x - 4)\) Aftrekken 00kv - Logaritmen herleiden - basis - eind - 1ms - dynamic variables b \({}^{2}\!\log(x) - {}^{2}\!\log(5 x - 4)\) 1p 2p c \(3 ⋅ {}^{5}\!\log(2 x)\) Vermenigvuldigen 00kw - Logaritmen herleiden - basis - midden - 0ms - dynamic variables c \(3 ⋅ {}^{5}\!\log(2 x)\) 1p ○ \(\text{ } = {}^{5}\!\log(8 x^{3})\) 1p 2p d \(5 ⋅ {}^{4}\!\log(p) + {}^{4}\!\log(2 p + 3)\) OptellenVermenigvuldigen 00kx - Logaritmen herleiden - basis - eind - 0ms - dynamic variables d \(5 ⋅ {}^{4}\!\log(p) + {}^{4}\!\log(2 p + 3)\) 1p ○ \(\text{ } = {}^{4}\!\log(p^{5} ⋅ (2 p + 3))\) 1p opgave 2Herleid tot één logaritme. 2p a \(3 + {}^{2}\!\log(a + 4)\) Grondtal (1) 00ky - Logaritmen herleiden - basis - midden - 0ms - dynamic variables a \(3 + {}^{2}\!\log(a + 4)\) 1p ○ \(\text{ } = {}^{2}\!\log(8 ⋅ (a + 4))\) 1p 3p b \({}^{4}\!\log(64) + {}^{5}\!\log(x - 2)\) Grondtal (2) 00kz - Logaritmen herleiden - basis - eind - 0ms - dynamic variables b \({}^{4}\!\log(64) + {}^{5}\!\log(x - 2)\) 1p ○ \(\text{ } = {}^{5}\!\log(5^{3}) + {}^{5}\!\log(x - 2)\) 1p ○ \(\text{ } = {}^{5}\!\log(125 ⋅ (x - 2))\) 1p |