Logaritmische formules herleiden

0w - 11 oefeningen

Dubbel (1) 00ks - Logaritmische formules herleiden - basis - 0ms - dynamic variables	Getal & Ruimte (12e editie) - havo wiskunde B - 9.4
Herleid tot de gevraagde vorm. 3p Schrijf de formule \(y = 770 x^{-1{,}68}\) in de vorm \(\log(y) = a + b ⋅ \log(x) \text{.}\) Geef \(a\) in twee decimalen.	○ \(y = 770 x^{-1{,}68}\) \(\log(y) = \log(770 x^{-1{,}68})\) 1p ○ \(\log(y) = \log(770) + \log(x^{-1{,}68})\) \(\log(y) = \log(770) - 1{,}68 ⋅ \log(x)\) 1p ○ \(\log(y) = 2{,}886... - 1{,}68 ⋅ \log(x)\) Dus \(y = 2{,}89 - 1{,}68 ⋅ \log(x) \text{.}\) 1p
Dubbel (2) 00kt - Logaritmische formules herleiden - basis - 0ms - dynamic variables	Getal & Ruimte (12e editie) - havo wiskunde B - 9.4
Herleid tot de gevraagde vorm. 3p Schrijf de formule \(y = {450 \over x^{2} \sqrt{x}}\) in de vorm \(\log(y) = a + b ⋅ \log(x) \text{.}\) Geef \(a\) in twee decimalen.	○ \(y = {450 \over x^{2} \sqrt{x}} = 450 x^{-2{,}5}\) \(\log(y) = \log(450 x^{-2{,}5})\) 1p ○ \(\log(y) = \log(450) + \log(x^{-2{,}5})\) \(\log(y) = \log(450) - 2{,}5 ⋅ \log(x)\) 1p ○ \(\log(y) = 2{,}653... - 2{,}5 ⋅ \log(x)\) Dus \(y = 2{,}65 - 2{,}5 ⋅ \log(x) \text{.}\) 1p
Dubbel (3) 00kr - Logaritmische formules herleiden - basis - 0ms - dynamic variables	Getal & Ruimte (12e editie) - havo wiskunde B - 9.4
Herleid tot de gevraagde vorm. 3p Schrijf de formule \(\log(y) = 3{,}12 - 1{,}12 ⋅ \log(x)\) in de vorm \(y = a x^{b} \text{.}\) Geef \(a\) in gehelen.	○ \(\log(y) = 3{,}12 - 1{,}12 ⋅ \log(x)\) \(\log(y) = \log(10^{3{,}12}) + \log(x^{-1{,}12})\) \(\log(y) = \log(10^{3{,}12} ⋅ x^{-1{,}12})\) 1p ○ \(y = 10^{3{,}12} ⋅ x^{-1{,}12}\) 1p ○ \(y = 1318{,}256... ⋅ x^{-1{,}12}\) Dus \(y = 1\,318 ⋅ x^{-1{,}12} \text{.}\) 1p
Herleiden (1) 00ko - Logaritmische formules herleiden - basis - 0ms - dynamic variables	Getal & Ruimte (12e editie) - havo wiskunde B - 9.4 Getal & Ruimte (12e editie) - vwo wiskunde A - 13.4
Herleid tot de gevraagde vorm. 3p Schrijf de formule \(y = 4\,400 ⋅ 0{,}74^{x}\) in de vorm \(\log(y) = a x + b \text{.}\) Geef \(a\) in vier decimalen en \(b\) in twee decimalen.	○ \(y = 4\,400 ⋅ 0{,}74^{x}\) \(\log(y) = \log(4\,400 ⋅ 0{,}74^{x})\) \(\log(y) = \log(4\,400) + \log(0{,}74^{x})\) 1p ○ \(\log(y) = \log(4\,400) + x ⋅ \log(0{,}74)\) 1p ○ \(\log(y) = 3{,}643... + x ⋅ -0{,}13076...\) Dus \(\log(y) = -0{,}1308 x + 3{,}64\) 1p
Herleiden (2) 00kp - Logaritmische formules herleiden - basis - 1ms - dynamic variables	Getal & Ruimte (12e editie) - havo wiskunde B - 9.4 Getal & Ruimte (12e editie) - vwo wiskunde A - 13.4
Herleid tot de gevraagde vorm. 3p Schrijf de formule \(y = 7\,500 ⋅ 0{,}83^{5 x + 3}\) in de vorm \(\log(y) = a x + b \text{.}\) Geef \(a\) in vier decimalen en \(b\) in twee decimalen.	○ \(y = 7\,500 ⋅ 0{,}83^{5 x + 3}\) \(\log(y) = \log(7\,500 ⋅ 0{,}83^{5 x + 3})\) \(\log(y) = \log(7\,500) + \log(0{,}83^{5 x + 3})\) 1p ○ \(\log(y) = \log(7\,500) + (5 x + 3) ⋅ \log(0{,}83)\) \(\log(y) = \log(7\,500) + 5 x ⋅ \log(0{,}83) + 3 ⋅ \log(0{,}83)\) 1p ○ \(\log(y) = 3{,}875... + 5 x ⋅ -0{,}08092... + 3 ⋅ -0{,}08092...\) \(\log(y) = 3{,}875... - 0{,}40460... ⋅ x - 0{,}24276...\) Dus \(\log(y) = -0{,}4046 x + 3{,}63\) 1p
Herleiden (3) 00kq - Logaritmische formules herleiden - basis - 0ms - dynamic variables	Getal & Ruimte (12e editie) - havo wiskunde B - 9.4 Getal & Ruimte (12e editie) - vwo wiskunde A - 13.4
Herleid tot de gevraagde vorm. 3p Schrijf de formule \(\log(y) = -0{,}9398 x + 2{,}41\) in de vorm \(y = b ⋅ g^{x} \text{.}\) Geef \(b\) in gehelen en \(g\) in twee decimalen.	○ \(\log(y) = -0{,}9398 x + 2{,}41\) \(y = 10^{-0{,}9398 x + 2{,}41}\) 1p ○ \(y = 10^{-0{,}9398 x} ⋅ 10^{2{,}41}\) \(y = (10^{-0{,}9398})^{x} ⋅ 10^{2{,}41}\) 1p ○ \(y = 0{,}114...^{x} ⋅ 257{,}039...\) Dus \(y = 257 ⋅ 0{,}11^{x} \text{.}\) 1p
Herleiden (4) 00l0 - Logaritmische formules herleiden - basis - 0ms - dynamic variables	Getal & Ruimte (12e editie) - havo wiskunde B - 9.3
Herleid tot de gevraagde vorm. 3p Schrijf de formule \(y = 1{,}37 ⋅ {}^{5}\!\log(x) - 2{,}36\) in de vorm \(y = {}^{5}\!\log(a x^{b}) \text{.}\) Geef \(a\) en \(b\) in twee decimalen.	○ \(y = 1{,}37 ⋅ {}^{5}\!\log(x) - 2{,}36\) \(\text{ } = {}^{5}\!\log(x^{1{,}37}) - 2{,}36\) 1p ○ \(\text{ } = {}^{5}\!\log(x^{1{,}37}) + {}^{5}\!\log(5^{-2{,}36})\) \(\text{ } = {}^{5}\!\log(x^{1{,}37} ⋅ 5^{-2{,}36})\) 1p ○ \(\text{ } = {}^{5}\!\log(x^{1{,}37} ⋅ 0{,}022...)\) Dus \(y = {}^{5}\!\log(0{,}02 ⋅ x^{1{,}37}) \text{.}\) 1p
Herleiden (6) 00l2 - Logaritmische formules herleiden - basis - 0ms - dynamic variables	Getal & Ruimte (12e editie) - havo wiskunde B - 9.3 Getal & Ruimte (12e editie) - vwo wiskunde A - 13.4
Herleid tot de gevraagde vorm. 3p Schrijf de formule \(y = {}^{4}\!\log(1{,}6 x) + 1{,}2\) in de vorm \(y = a + b ⋅ {}^{5}\!\log(x) \text{.}\) Geef \(a\) en \(b\) in twee decimalen.	○ \(y = {}^{4}\!\log(1{,}6 x) + 1{,}2\) \(\text{ } = {}^{4}\!\log(1{,}6) + {}^{4}\!\log(x) + 1{,}2\) 1p ○ \(\text{ } = {}^{4}\!\log(1{,}6) + 1{,}2 + {{}^{5}\!\log(x) \over {}^{5}\!\log(4)}\) \(\text{ } = {}^{4}\!\log(1{,}6) + 1{,}2 + {1 \over {}^{5}\!\log(4)} ⋅ {}^{5}\!\log(x)\) 1p ○ \(\text{ } = 0{,}339... + 1{,}2 + {1 \over 0{,}861...} ⋅ {}^{5}\!\log(x)\) \(\text{ } = 1{,}539... + 1{,}160... ⋅ {}^{5}\!\log(x)\) Dus \(y = 1{,}54 + 1{,}16 ⋅ {}^{5}\!\log(x) \text{.}\) 1p
Herleiden (7) 00l3 - Logaritmische formules herleiden - basis - 1ms - dynamic variables	Getal & Ruimte (12e editie) - havo wiskunde B - 9.3
Herleid tot de gevraagde vorm. 3p Schrijf de formule \(y = 9 ⋅ \log(2\,000 x) - 5\) in de vorm \(y = a + b ⋅ \log(2 x) \text{.}\)	○ \(y = 9 ⋅ \log(2\,000 x) - 5\) \(\text{ } = 9 ⋅ (\log(1\,000) + \log(2 x)) - 5\) 1p ○ \(\text{ } = 9 ⋅ (3 + \log(2 x)) - 5\) 1p ○ \(\text{ } = 27 + 9 ⋅ \log(2 x) - 5\) \(\text{ } = 22 + 9 ⋅ \log(2 x)\) 1p
Logaritmisch (5) 00l1 - Logaritmische formules herleiden - basis - 0ms - dynamic variables	Getal & Ruimte (12e editie) - havo wiskunde B - 9.3
Herleid tot de gevraagde vorm. 3p Schrijf de formule \(y = {}^{3}\!\log(71 x^{5})\) in de vorm \(y = a + b ⋅ {}^{3}\!\log(x) \text{.}\) Geef \(a\) in twee decimalen.	○ \(y = {}^{3}\!\log(71 x^{5})\) \(\text{ } = {}^{3}\!\log(71 x^{5})\) 1p ○ \(\text{ } = {}^{3}\!\log(71) + {}^{3}\!\log(x^{5})\) \(\text{ } = {}^{3}\!\log(71) + 5 ⋅ {}^{3}\!\log(x)\) 1p ○ \(\text{ } = 3{,}880... + 5 ⋅ {}^{3}\!\log(x)\) Dus \(y = 3{,}88 + 5 ⋅ {}^{3}\!\log(x) \text{.}\) 1p
Vrijmaken 00kn - Logaritmische formules herleiden - basis - 1ms - dynamic variables	Getal & Ruimte (12e editie) - havo wiskunde B - 9.2 Getal & Ruimte (12e editie) - vwo wiskunde A - 13.4 Getal & Ruimte (12e editie) - vwo wiskunde B - 9.2
Druk \(x\) uit in \(y \text{.}\) 3p \(y = 12 + 3 ⋅ {}^{5}\!\log(2 x + 8)\)	○ \(y = 12 + 3 ⋅ {}^{5}\!\log(2 x + 8)\) \(3 ⋅ {}^{5}\!\log(2 x + 8) = y - 12\) \({}^{5}\!\log(2 x + 8) = \frac{1}{3} y - 4\) 1p ○ \(2 x + 8 = 5^{\frac{1}{3} y - 4}\) 1p ○ \(2 x = 5^{\frac{1}{3} y - 4} - 8\) \(x = \frac{1}{2} ⋅ 5^{\frac{1}{3} y - 4} - 4\) 1p

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