Getal & Ruimte (13e editie) - havo wiskunde B

'Logaritmische formules herleiden'.

havo wiskunde B	9.2 Werken met logaritmen
Logaritmische formules herleiden (1)	opgave 1 Druk \(x\) uit in \(y \text{.}\) 3p \(y = 21 + 3 ⋅ {}^{2}\!\log(5 x + 8)\) Vrijmaken 00kn - Logaritmische formules herleiden - basis - 0ms - dynamic variables ○ \(y = 21 + 3 ⋅ {}^{2}\!\log(5 x + 8)\) \(3 ⋅ {}^{2}\!\log(5 x + 8) = y - 21\) \({}^{2}\!\log(5 x + 8) = \frac{1}{3} y - 7\) 1p ○ \(5 x + 8 = 2^{\frac{1}{3} y - 7}\) 1p ○ \(5 x = 2^{\frac{1}{3} y - 7} - 8\) \(x = \frac{1}{5} ⋅ 2^{\frac{1}{3} y - 7} - 1\frac{3}{5}\) 1p
havo wiskunde B	9.3 Rekenregels voor logaritmen
Logaritmische formules herleiden (4)	opgave 1 Herleid tot de gevraagde vorm. 3p a Schrijf de formule \(y = 2{,}83 ⋅ {}^{2}\!\log(x) - 2{,}42\) in de vorm \(y = {}^{2}\!\log(a x^{b}) \text{.}\) Geef \(a\) en \(b\) in twee decimalen. Herleiden (4) 00l0 - Logaritmische formules herleiden - basis - 0ms - dynamic variables a \(y = 2{,}83 ⋅ {}^{2}\!\log(x) - 2{,}42\) \(\text{ } = {}^{2}\!\log(x^{2{,}83}) - 2{,}42\) 1p ○ \(\text{ } = {}^{2}\!\log(x^{2{,}83}) + {}^{2}\!\log(2^{-2{,}42})\) \(\text{ } = {}^{2}\!\log(x^{2{,}83} ⋅ 2^{-2{,}42})\) 1p ○ \(\text{ } = {}^{2}\!\log(x^{2{,}83} ⋅ 0{,}186...)\) Dus \(y = {}^{2}\!\log(0{,}19 ⋅ x^{2{,}83}) \text{.}\) 1p 3p b Schrijf de formule \(y = {}^{3}\!\log(68 x^{2})\) in de vorm \(y = a + b ⋅ {}^{3}\!\log(x) \text{.}\) Geef \(a\) in twee decimalen. Herleiden (5) 00l1 - Logaritmische formules herleiden - basis - 0ms - dynamic variables b \(y = {}^{3}\!\log(68 x^{2})\) \(\text{ } = {}^{3}\!\log(68 x^{2})\) 1p ○ \(\text{ } = {}^{3}\!\log(68) + {}^{3}\!\log(x^{2})\) \(\text{ } = {}^{3}\!\log(68) + 2 ⋅ {}^{3}\!\log(x)\) 1p ○ \(\text{ } = 3{,}840... + 2 ⋅ {}^{3}\!\log(x)\) Dus \(y = 3{,}84 + 2 ⋅ {}^{3}\!\log(x) \text{.}\) 1p 3p c Schrijf de formule \(y = {}^{2}\!\log(1{,}8 x) - 0{,}4\) in de vorm \(y = a + b ⋅ {}^{3}\!\log(x) \text{.}\) Geef \(a\) en \(b\) in twee decimalen. Herleiden (6) 00l2 - Logaritmische formules herleiden - basis - 0ms - dynamic variables c \(y = {}^{2}\!\log(1{,}8 x) - 0{,}4\) \(\text{ } = {}^{2}\!\log(1{,}8) + {}^{2}\!\log(x) - 0{,}4\) 1p ○ \(\text{ } = {}^{2}\!\log(1{,}8) - 0{,}4 + {{}^{3}\!\log(x) \over {}^{3}\!\log(2)}\) \(\text{ } = {}^{2}\!\log(1{,}8) - 0{,}4 + {1 \over {}^{3}\!\log(2)} ⋅ {}^{3}\!\log(x)\) 1p ○ \(\text{ } = 0{,}847... - 0{,}4 + {1 \over 0{,}630...} ⋅ {}^{3}\!\log(x)\) \(\text{ } = 0{,}447... + 1{,}584... ⋅ {}^{3}\!\log(x)\) Dus \(y = 0{,}45 + 1{,}58 ⋅ {}^{3}\!\log(x) \text{.}\) 1p 3p d Schrijf de formule \(y = 5 ⋅ {}^{3}\!\log(36 x) - 10\) in de vorm \(y = a + b ⋅ {}^{3}\!\log(4 x) \text{.}\) Herleiden (7) 00l3 - Logaritmische formules herleiden - basis - 0ms - dynamic variables d \(y = 5 ⋅ {}^{3}\!\log(36 x) - 10\) \(\text{ } = 5 ⋅ ({}^{3}\!\log(9) + {}^{3}\!\log(4 x)) - 10\) 1p ○ \(\text{ } = 5 ⋅ (2 + {}^{3}\!\log(4 x)) - 10\) 1p ○ \(\text{ } = 10 + 5 ⋅ {}^{3}\!\log(4 x) - 10\) \(\text{ } = 0 + 5 ⋅ {}^{3}\!\log(4 x)\) 1p

"