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 \(y = 660 x^{-1{,}13}\) in de vorm \(\log(y) = a + b ⋅ \log(x) \text{.}\) Geef \(a\) in twee decimalen.	○ \(y = 660 x^{-1{,}13}\) \(\log(y) = \log(660 x^{-1{,}13})\) 1p ○ \(\log(y) = \log(660) + \log(x^{-1{,}13})\) \(\log(y) = \log(660) - 1{,}13 ⋅ \log(x)\) 1p ○ \(\log(y) = 2{,}819... - 1{,}13 ⋅ \log(x)\) Dus \(y = 2{,}82 - 1{,}13 ⋅ \log(x) \text{.}\) 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 \(y = {90 \over x^{4}}\) in de vorm \(\log(y) = a + b ⋅ \log(x) \text{.}\) Geef \(a\) in twee decimalen.	○ \(y = {90 \over x^{4}} = 90 x^{-4}\) \(\log(y) = \log(90 x^{-4})\) 1p ○ \(\log(y) = \log(90) + \log(x^{-4})\) \(\log(y) = \log(90) - 4 ⋅ \log(x)\) 1p ○ \(\log(y) = 1{,}954... - 4 ⋅ \log(x)\) Dus \(y = 1{,}95 - 4 ⋅ \log(x) \text{.}\) 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 \(\log(y) = 3{,}35 - 1{,}52 ⋅ \log(x)\) in de vorm \(y = a x^{b} \text{.}\) Geef \(a\) in gehelen.	○ \(\log(y) = 3{,}35 - 1{,}52 ⋅ \log(x)\) \(\log(y) = \log(10^{3{,}35}) + \log(x^{-1{,}52})\) \(\log(y) = \log(10^{3{,}35} ⋅ x^{-1{,}52})\) 1p ○ \(y = 10^{3{,}35} ⋅ x^{-1{,}52}\) 1p ○ \(y = 2238{,}721... ⋅ x^{-1{,}52}\) Dus \(y = 2\,239 ⋅ x^{-1{,}52} \text{.}\) 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 \(y = 2\,300 ⋅ 0{,}86^{x}\) in de vorm \(\log(y) = a x + b \text{.}\) Geef \(a\) in vier decimalen en \(b\) in twee decimalen.	○ \(y = 2\,300 ⋅ 0{,}86^{x}\) \(\log(y) = \log(2\,300 ⋅ 0{,}86^{x})\) \(\log(y) = \log(2\,300) + \log(0{,}86^{x})\) 1p ○ \(\log(y) = \log(2\,300) + x ⋅ \log(0{,}86)\) 1p ○ \(\log(y) = 3{,}361... + x ⋅ -0{,}06550...\) Dus \(\log(y) = -0{,}0655 x + 3{,}36\) 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 \(y = 7\,600 ⋅ 1{,}25^{5 x + 2}\) in de vorm \(\log(y) = a x + b \text{.}\) Geef \(a\) in vier decimalen en \(b\) in twee decimalen.	○ \(y = 7\,600 ⋅ 1{,}25^{5 x + 2}\) \(\log(y) = \log(7\,600 ⋅ 1{,}25^{5 x + 2})\) \(\log(y) = \log(7\,600) + \log(1{,}25^{5 x + 2})\) 1p ○ \(\log(y) = \log(7\,600) + (5 x + 2) ⋅ \log(1{,}25)\) \(\log(y) = \log(7\,600) + 5 x ⋅ \log(1{,}25) + 2 ⋅ \log(1{,}25)\) 1p ○ \(\log(y) = 3{,}880... + 5 x ⋅ 0{,}09691... + 2 ⋅ 0{,}09691...\) \(\log(y) = 3{,}880... + 0{,}48455... ⋅ x + 0{,}19382...\) Dus \(\log(y) = 0{,}4846 x + 4{,}07\) 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 \(\log(y) = -0{,}4435 x + 1{,}16\) in de vorm \(y = b ⋅ g^{x} \text{.}\) Geef \(b\) in gehelen en \(g\) in twee decimalen.	○ \(\log(y) = -0{,}4435 x + 1{,}16\) \(y = 10^{-0{,}4435 x + 1{,}16}\) 1p ○ \(y = 10^{-0{,}4435 x} ⋅ 10^{1{,}16}\) \(y = (10^{-0{,}4435})^{x} ⋅ 10^{1{,}16}\) 1p ○ \(y = 0{,}360...^{x} ⋅ 14{,}454...\) Dus \(y = 14 ⋅ 0{,}36^{x} \text{.}\) 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 \(y = 1{,}84 ⋅ {}^{2}\!\log(x) + 1{,}14\) in de vorm \(y = {}^{2}\!\log(a x^{b}) \text{.}\) Geef \(a\) en \(b\) in twee decimalen.	○ \(y = 1{,}84 ⋅ {}^{2}\!\log(x) + 1{,}14\) \(\text{ } = {}^{2}\!\log(x^{1{,}84}) + 1{,}14\) 1p ○ \(\text{ } = {}^{2}\!\log(x^{1{,}84}) + {}^{2}\!\log(2^{1{,}14})\) \(\text{ } = {}^{2}\!\log(x^{1{,}84} ⋅ 2^{1{,}14})\) 1p ○ \(\text{ } = {}^{2}\!\log(x^{1{,}84} ⋅ 2{,}203...)\) Dus \(y = {}^{2}\!\log(2{,}20 ⋅ x^{1{,}84}) \text{.}\) 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 \(y = {}^{5}\!\log(1{,}8 x) - 1{,}4\) in de vorm \(y = a + b ⋅ {}^{3}\!\log(x) \text{.}\) Geef \(a\) en \(b\) in twee decimalen.	○ \(y = {}^{5}\!\log(1{,}8 x) - 1{,}4\) \(\text{ } = {}^{5}\!\log(1{,}8) + {}^{5}\!\log(x) - 1{,}4\) 1p ○ \(\text{ } = {}^{5}\!\log(1{,}8) - 1{,}4 + {{}^{3}\!\log(x) \over {}^{3}\!\log(5)}\) \(\text{ } = {}^{5}\!\log(1{,}8) - 1{,}4 + {1 \over {}^{3}\!\log(5)} ⋅ {}^{3}\!\log(x)\) 1p ○ \(\text{ } = 0{,}365... - 1{,}4 + {1 \over 1{,}464...} ⋅ {}^{3}\!\log(x)\) \(\text{ } = -1{,}034... + 0{,}682... ⋅ {}^{3}\!\log(x)\) Dus \(y = -1{,}03 + 0{,}68 ⋅ {}^{3}\!\log(x) \text{.}\) 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 \(y = 5 ⋅ \log(400 x) - 6\) in de vorm \(y = a + b ⋅ \log(4 x) \text{.}\)	○ \(y = 5 ⋅ \log(400 x) - 6\) \(\text{ } = 5 ⋅ (\log(100) + \log(4 x)) - 6\) 1p ○ \(\text{ } = 5 ⋅ (2 + \log(4 x)) - 6\) 1p ○ \(\text{ } = 10 + 5 ⋅ \log(4 x) - 6\) \(\text{ } = 4 + 5 ⋅ \log(4 x)\) 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 \(y = {}^{2}\!\log({55 \over x^{3}})\) in de vorm \(y = a + b ⋅ {}^{2}\!\log(x) \text{.}\) Geef \(a\) in twee decimalen.	○ \(y = {}^{2}\!\log({55 \over x^{3}})\) \(\text{ } = {}^{2}\!\log(55 x^{-3})\) 1p ○ \(\text{ } = {}^{2}\!\log(55) + {}^{2}\!\log(x^{-3})\) \(\text{ } = {}^{2}\!\log(55) - 3 ⋅ {}^{2}\!\log(x)\) 1p ○ \(\text{ } = 5{,}781... - 3 ⋅ {}^{2}\!\log(x)\) Dus \(y = 5{,}78 - 3 ⋅ {}^{2}\!\log(x) \text{.}\) 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 \(y = 10 + 2 ⋅ {}^{9}\!\log(8 x - 4)\)	○ \(y = 10 + 2 ⋅ {}^{9}\!\log(8 x - 4)\) \(2 ⋅ {}^{9}\!\log(8 x - 4) = y - 10\) \({}^{9}\!\log(8 x - 4) = \frac{1}{2} y - 5\) 1p ○ \(8 x - 4 = 9^{\frac{1}{2} y - 5}\) 1p ○ \(8 x = 9^{\frac{1}{2} y - 5} + 4\) \(x = \frac{1}{8} ⋅ 9^{\frac{1}{2} y - 5} + \frac{1}{2}\) 1p

00ks 00kt 00kr 00ko 00kp 00kq 00l0 00l2 00l3 00l1 00kn