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 \(y = 200 x^{-1{,}68}\) in de vorm \(\log(y) = a + b ⋅ \log(x) \text{.}\) Geef \(a\) in twee decimalen.	○ \(y = 200 x^{-1{,}68}\) \(\log(y) = \log(200 x^{-1{,}68})\) 1p ○ \(\log(y) = \log(200) + \log(x^{-1{,}68})\) \(\log(y) = \log(200) - 1{,}68 ⋅ \log(x)\) 1p ○ \(\log(y) = 2{,}301... - 1{,}68 ⋅ \log(x)\) Dus \(y = 2{,}30 - 1{,}68 ⋅ \log(x) \text{.}\) 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 \(y = {580 \over x^{4}}\) in de vorm \(\log(y) = a + b ⋅ \log(x) \text{.}\) Geef \(a\) in twee decimalen.	○ \(y = {580 \over x^{4}} = 580 x^{-4}\) \(\log(y) = \log(580 x^{-4})\) 1p ○ \(\log(y) = \log(580) + \log(x^{-4})\) \(\log(y) = \log(580) - 4 ⋅ \log(x)\) 1p ○ \(\log(y) = 2{,}763... - 4 ⋅ \log(x)\) Dus \(y = 2{,}76 - 4 ⋅ \log(x) \text{.}\) 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 \(\log(y) = 1{,}38 - 1{,}84 ⋅ \log(x)\) in de vorm \(y = a x^{b} \text{.}\) Geef \(a\) in gehelen.	○ \(\log(y) = 1{,}38 - 1{,}84 ⋅ \log(x)\) \(\log(y) = \log(10^{1{,}38}) + \log(x^{-1{,}84})\) \(\log(y) = \log(10^{1{,}38} ⋅ x^{-1{,}84})\) 1p ○ \(y = 10^{1{,}38} ⋅ x^{-1{,}84}\) 1p ○ \(y = 23{,}988... ⋅ x^{-1{,}84}\) Dus \(y = 24 ⋅ x^{-1{,}84} \text{.}\) 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 \(y = 1\,400 ⋅ 0{,}92^{x}\) in de vorm \(\log(y) = a x + b \text{.}\) Geef \(a\) in vier decimalen en \(b\) in twee decimalen.	○ \(y = 1\,400 ⋅ 0{,}92^{x}\) \(\log(y) = \log(1\,400 ⋅ 0{,}92^{x})\) \(\log(y) = \log(1\,400) + \log(0{,}92^{x})\) 1p ○ \(\log(y) = \log(1\,400) + x ⋅ \log(0{,}92)\) 1p ○ \(\log(y) = 3{,}146... + x ⋅ -0{,}03621...\) Dus \(\log(y) = -0{,}0362 x + 3{,}15\) 1p
Herleiden (2) 00kp - 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 \(y = 5\,300 ⋅ 0{,}91^{3 x + 2}\) in de vorm \(\log(y) = a x + b \text{.}\) Geef \(a\) in vier decimalen en \(b\) in twee decimalen.	○ \(y = 5\,300 ⋅ 0{,}91^{3 x + 2}\) \(\log(y) = \log(5\,300 ⋅ 0{,}91^{3 x + 2})\) \(\log(y) = \log(5\,300) + \log(0{,}91^{3 x + 2})\) 1p ○ \(\log(y) = \log(5\,300) + (3 x + 2) ⋅ \log(0{,}91)\) \(\log(y) = \log(5\,300) + 3 x ⋅ \log(0{,}91) + 2 ⋅ \log(0{,}91)\) 1p ○ \(\log(y) = 3{,}724... + 3 x ⋅ -0{,}04095... + 2 ⋅ -0{,}04095...\) \(\log(y) = 3{,}724... - 0{,}12287... ⋅ x - 0{,}08191...\) Dus \(\log(y) = -0{,}1229 x + 3{,}64\) 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 \(\log(y) = -0{,}6534 x + 1{,}04\) in de vorm \(y = b ⋅ g^{x} \text{.}\) Geef \(b\) in gehelen en \(g\) in twee decimalen.	○ \(\log(y) = -0{,}6534 x + 1{,}04\) \(y = 10^{-0{,}6534 x + 1{,}04}\) 1p ○ \(y = 10^{-0{,}6534 x} ⋅ 10^{1{,}04}\) \(y = (10^{-0{,}6534})^{x} ⋅ 10^{1{,}04}\) 1p ○ \(y = 0{,}222...^{x} ⋅ 10{,}964...\) Dus \(y = 11 ⋅ 0{,}22^{x} \text{.}\) 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 \(y = 1{,}63 ⋅ {}^{5}\!\log(x) - 2{,}75\) in de vorm \(y = {}^{5}\!\log(a x^{b}) \text{.}\) Geef \(a\) en \(b\) in twee decimalen.	○ \(y = 1{,}63 ⋅ {}^{5}\!\log(x) - 2{,}75\) \(\text{ } = {}^{5}\!\log(x^{1{,}63}) - 2{,}75\) 1p ○ \(\text{ } = {}^{5}\!\log(x^{1{,}63}) + {}^{5}\!\log(5^{-2{,}75})\) \(\text{ } = {}^{5}\!\log(x^{1{,}63} ⋅ 5^{-2{,}75})\) 1p ○ \(\text{ } = {}^{5}\!\log(x^{1{,}63} ⋅ 0{,}011...)\) Dus \(y = {}^{5}\!\log(0{,}01 ⋅ x^{1{,}63}) \text{.}\) 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 \(y = {}^{5}\!\log(1{,}7 x) + 0{,}3\) in de vorm \(y = a + b ⋅ {}^{2}\!\log(x) \text{.}\) Geef \(a\) en \(b\) in twee decimalen.	○ \(y = {}^{5}\!\log(1{,}7 x) + 0{,}3\) \(\text{ } = {}^{5}\!\log(1{,}7) + {}^{5}\!\log(x) + 0{,}3\) 1p ○ \(\text{ } = {}^{5}\!\log(1{,}7) + 0{,}3 + {{}^{2}\!\log(x) \over {}^{2}\!\log(5)}\) \(\text{ } = {}^{5}\!\log(1{,}7) + 0{,}3 + {1 \over {}^{2}\!\log(5)} ⋅ {}^{2}\!\log(x)\) 1p ○ \(\text{ } = 0{,}329... + 0{,}3 + {1 \over 2{,}321...} ⋅ {}^{2}\!\log(x)\) \(\text{ } = 0{,}629... + 0{,}430... ⋅ {}^{2}\!\log(x)\) Dus \(y = 0{,}63 + 0{,}43 ⋅ {}^{2}\!\log(x) \text{.}\) 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 \(y = 9 ⋅ {}^{3}\!\log(36 x) + 8\) in de vorm \(y = a + b ⋅ {}^{3}\!\log(4 x) \text{.}\)	○ \(y = 9 ⋅ {}^{3}\!\log(36 x) + 8\) \(\text{ } = 9 ⋅ ({}^{3}\!\log(9) + {}^{3}\!\log(4 x)) + 8\) 1p ○ \(\text{ } = 9 ⋅ (2 + {}^{3}\!\log(4 x)) + 8\) 1p ○ \(\text{ } = 18 + 9 ⋅ {}^{3}\!\log(4 x) + 8\) \(\text{ } = 26 + 9 ⋅ {}^{3}\!\log(4 x)\) 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 \(y = {}^{5}\!\log(82 x^{3})\) in de vorm \(y = a + b ⋅ {}^{5}\!\log(x) \text{.}\) Geef \(a\) in twee decimalen.	○ \(y = {}^{5}\!\log(82 x^{3})\) \(\text{ } = {}^{5}\!\log(82 x^{3})\) 1p ○ \(\text{ } = {}^{5}\!\log(82) + {}^{5}\!\log(x^{3})\) \(\text{ } = {}^{5}\!\log(82) + 3 ⋅ {}^{5}\!\log(x)\) 1p ○ \(\text{ } = 2{,}738... + 3 ⋅ {}^{5}\!\log(x)\) Dus \(y = 2{,}74 + 3 ⋅ {}^{5}\!\log(x) \text{.}\) 1p
Vrijmaken 00kn - Logaritmische formules herleiden - basis - 0ms - 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 \(y = 2 + 2 ⋅ {}^{8}\!\log(9 x - 5)\)	○ \(y = 2 + 2 ⋅ {}^{8}\!\log(9 x - 5)\) \(2 ⋅ {}^{8}\!\log(9 x - 5) = y - 2\) \({}^{8}\!\log(9 x - 5) = \frac{1}{2} y - 1\) 1p ○ \(9 x - 5 = 8^{\frac{1}{2} y - 1}\) 1p ○ \(9 x = 8^{\frac{1}{2} y - 1} + 5\) \(x = \frac{1}{9} ⋅ 8^{\frac{1}{2} y - 1} + \frac{5}{9}\) 1p

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