Getal & Ruimte (12e editie) - havo wiskunde B
'Logaritmen herleiden'.
| havo wiskunde B | 9.3 Rekenregels voor logaritmen |
opgave 1Herleid tot één logaritme. 1p a \({}^{2}\!\log(5 a) + {}^{2}\!\log(3 a + 1)\) Optellen (1) 00ku - Logaritmen herleiden - basis - basis - 1ms - dynamic variables a \({}^{2}\!\log(5 a) + {}^{2}\!\log(3 a + 1)\) 1p 1p b \({}^{3}\!\log(2 x) - {}^{3}\!\log(4 x - 1)\) Aftrekken 00kv - Logaritmen herleiden - basis - eind - 1ms - dynamic variables b \({}^{3}\!\log(2 x) - {}^{3}\!\log(4 x - 1)\) 1p 2p c \(4 ⋅ {}^{3}\!\log(5 p)\) Vermenigvuldigen 00kw - Logaritmen herleiden - basis - midden - 1ms - dynamic variables c \(4 ⋅ {}^{3}\!\log(5 p)\) 1p ○ \(\text{ } = {}^{3}\!\log(625 p^{4})\) 1p 2p d \(5 ⋅ {}^{2}\!\log(x) + {}^{2}\!\log(4 x + 3)\) OptellenVermenigvuldigen 00kx - Logaritmen herleiden - basis - eind - 1ms - dynamic variables d \(5 ⋅ {}^{2}\!\log(x) + {}^{2}\!\log(4 x + 3)\) 1p ○ \(\text{ } = {}^{2}\!\log(x^{5} ⋅ (4 x + 3))\) 1p opgave 2Herleid tot één logaritme. 2p a \(5 + {}^{4}\!\log(3 a + 2)\) Grondtal (1) 00ky - Logaritmen herleiden - basis - midden - 1ms - dynamic variables a \(5 + {}^{4}\!\log(3 a + 2)\) 1p ○ \(\text{ } = {}^{4}\!\log(1\,024 ⋅ (3 a + 2))\) 1p 3p b \({}^{4}\!\log(1\,024) + {}^{3}\!\log(2 x - 1)\) Grondtal (2) 00kz - Logaritmen herleiden - basis - eind - 1ms - dynamic variables b \({}^{4}\!\log(1\,024) + {}^{3}\!\log(2 x - 1)\) 1p ○ \(\text{ } = {}^{3}\!\log(3^{5}) + {}^{3}\!\log(2 x - 1)\) 1p ○ \(\text{ } = {}^{3}\!\log(243 ⋅ (2 x - 1))\) 1p |