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 \(y = 40 x^{-1{,}08}\) in de vorm \(\log(y) = a + b ⋅ \log(x) \text{.}\) Geef \(a\) in twee decimalen.	○ \(y = 40 x^{-1{,}08}\) \(\log(y) = \log(40 x^{-1{,}08})\) 1p ○ \(\log(y) = \log(40) + \log(x^{-1{,}08})\) \(\log(y) = \log(40) - 1{,}08 ⋅ \log(x)\) 1p ○ \(\log(y) = 1{,}602... - 1{,}08 ⋅ \log(x)\) Dus \(y = 1{,}60 - 1{,}08 ⋅ \log(x) \text{.}\) 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 \(y = {840 \over x^{2} \sqrt{x}}\) in de vorm \(\log(y) = a + b ⋅ \log(x) \text{.}\) Geef \(a\) in twee decimalen.	○ \(y = {840 \over x^{2} \sqrt{x}} = 840 x^{-2{,}5}\) \(\log(y) = \log(840 x^{-2{,}5})\) 1p ○ \(\log(y) = \log(840) + \log(x^{-2{,}5})\) \(\log(y) = \log(840) - 2{,}5 ⋅ \log(x)\) 1p ○ \(\log(y) = 2{,}924... - 2{,}5 ⋅ \log(x)\) Dus \(y = 2{,}92 - 2{,}5 ⋅ \log(x) \text{.}\) 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 \(\log(y) = 3{,}67 - 1{,}99 ⋅ \log(x)\) in de vorm \(y = a x^{b} \text{.}\) Geef \(a\) in gehelen.	○ \(\log(y) = 3{,}67 - 1{,}99 ⋅ \log(x)\) \(\log(y) = \log(10^{3{,}67}) + \log(x^{-1{,}99})\) \(\log(y) = \log(10^{3{,}67} ⋅ x^{-1{,}99})\) 1p ○ \(y = 10^{3{,}67} ⋅ x^{-1{,}99}\) 1p ○ \(y = 4677{,}351... ⋅ x^{-1{,}99}\) Dus \(y = 4\,677 ⋅ x^{-1{,}99} \text{.}\) 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 \(y = 3\,900 ⋅ 1{,}16^{x}\) in de vorm \(\log(y) = a x + b \text{.}\) Geef \(a\) in vier decimalen en \(b\) in twee decimalen.	○ \(y = 3\,900 ⋅ 1{,}16^{x}\) \(\log(y) = \log(3\,900 ⋅ 1{,}16^{x})\) \(\log(y) = \log(3\,900) + \log(1{,}16^{x})\) 1p ○ \(\log(y) = \log(3\,900) + x ⋅ \log(1{,}16)\) 1p ○ \(\log(y) = 3{,}591... + x ⋅ 0{,}06445...\) Dus \(\log(y) = 0{,}0645 x + 3{,}59\) 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 \(y = 3\,900 ⋅ 0{,}75^{2 x + 1}\) in de vorm \(\log(y) = a x + b \text{.}\) Geef \(a\) in vier decimalen en \(b\) in twee decimalen.	○ \(y = 3\,900 ⋅ 0{,}75^{2 x + 1}\) \(\log(y) = \log(3\,900 ⋅ 0{,}75^{2 x + 1})\) \(\log(y) = \log(3\,900) + \log(0{,}75^{2 x + 1})\) 1p ○ \(\log(y) = \log(3\,900) + (2 x + 1) ⋅ \log(0{,}75)\) \(\log(y) = \log(3\,900) + 2 x ⋅ \log(0{,}75) + 1 ⋅ \log(0{,}75)\) 1p ○ \(\log(y) = 3{,}591... + 2 x ⋅ -0{,}12493... + 1 ⋅ -0{,}12493...\) \(\log(y) = 3{,}591... - 0{,}24987... ⋅ x - 0{,}12493...\) Dus \(\log(y) = -0{,}2499 x + 3{,}47\) 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 \(\log(y) = 0{,}0993 x + 3{,}64\) in de vorm \(y = b ⋅ g^{x} \text{.}\) Geef \(b\) in gehelen en \(g\) in twee decimalen.	○ \(\log(y) = 0{,}0993 x + 3{,}64\) \(y = 10^{0{,}0993 x + 3{,}64}\) 1p ○ \(y = 10^{0{,}0993 x} ⋅ 10^{3{,}64}\) \(y = (10^{0{,}0993})^{x} ⋅ 10^{3{,}64}\) 1p ○ \(y = 1{,}256...^{x} ⋅ 4365{,}158...\) Dus \(y = 4\,365 ⋅ 1{,}26^{x} \text{.}\) 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 \(y = 3{,}93 ⋅ {}^{4}\!\log(x) - 1{,}45\) in de vorm \(y = {}^{4}\!\log(a x^{b}) \text{.}\) Geef \(a\) en \(b\) in twee decimalen.	○ \(y = 3{,}93 ⋅ {}^{4}\!\log(x) - 1{,}45\) \(\text{ } = {}^{4}\!\log(x^{3{,}93}) - 1{,}45\) 1p ○ \(\text{ } = {}^{4}\!\log(x^{3{,}93}) + {}^{4}\!\log(4^{-1{,}45})\) \(\text{ } = {}^{4}\!\log(x^{3{,}93} ⋅ 4^{-1{,}45})\) 1p ○ \(\text{ } = {}^{4}\!\log(x^{3{,}93} ⋅ 0{,}133...)\) Dus \(y = {}^{4}\!\log(0{,}13 ⋅ x^{3{,}93}) \text{.}\) 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 \(y = {}^{4}\!\log(2{,}2 x) - 1{,}6\) in de vorm \(y = a + b ⋅ {}^{5}\!\log(x) \text{.}\) Geef \(a\) en \(b\) in twee decimalen.	○ \(y = {}^{4}\!\log(2{,}2 x) - 1{,}6\) \(\text{ } = {}^{4}\!\log(2{,}2) + {}^{4}\!\log(x) - 1{,}6\) 1p ○ \(\text{ } = {}^{4}\!\log(2{,}2) - 1{,}6 + {{}^{5}\!\log(x) \over {}^{5}\!\log(4)}\) \(\text{ } = {}^{4}\!\log(2{,}2) - 1{,}6 + {1 \over {}^{5}\!\log(4)} ⋅ {}^{5}\!\log(x)\) 1p ○ \(\text{ } = 0{,}568... - 1{,}6 + {1 \over 0{,}861...} ⋅ {}^{5}\!\log(x)\) \(\text{ } = -1{,}031... + 1{,}160... ⋅ {}^{5}\!\log(x)\) Dus \(y = -1{,}03 + 1{,}16 ⋅ {}^{5}\!\log(x) \text{.}\) 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 \(y = 8 ⋅ {}^{4}\!\log(48 x) - 10\) in de vorm \(y = a + b ⋅ {}^{4}\!\log(3 x) \text{.}\)	○ \(y = 8 ⋅ {}^{4}\!\log(48 x) - 10\) \(\text{ } = 8 ⋅ ({}^{4}\!\log(16) + {}^{4}\!\log(3 x)) - 10\) 1p ○ \(\text{ } = 8 ⋅ (2 + {}^{4}\!\log(3 x)) - 10\) 1p ○ \(\text{ } = 16 + 8 ⋅ {}^{4}\!\log(3 x) - 10\) \(\text{ } = 6 + 8 ⋅ {}^{4}\!\log(3 x)\) 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 \(y = {}^{4}\!\log(77 x^{2} \sqrt{x})\) in de vorm \(y = a + b ⋅ {}^{4}\!\log(x) \text{.}\) Geef \(a\) in twee decimalen.	○ \(y = {}^{4}\!\log(77 x^{2} \sqrt{x})\) \(\text{ } = {}^{4}\!\log(77 x^{2{,}5})\) 1p ○ \(\text{ } = {}^{4}\!\log(77) + {}^{4}\!\log(x^{2{,}5})\) \(\text{ } = {}^{4}\!\log(77) + 2{,}5 ⋅ {}^{4}\!\log(x)\) 1p ○ \(\text{ } = 3{,}133... + 2{,}5 ⋅ {}^{4}\!\log(x)\) Dus \(y = 3{,}13 + 2{,}5 ⋅ {}^{4}\!\log(x) \text{.}\) 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 \(y = 6 + 2 ⋅ {}^{7}\!\log(5 x - 4)\)	○ \(y = 6 + 2 ⋅ {}^{7}\!\log(5 x - 4)\) \(2 ⋅ {}^{7}\!\log(5 x - 4) = y - 6\) \({}^{7}\!\log(5 x - 4) = \frac{1}{2} y - 3\) 1p ○ \(5 x - 4 = 7^{\frac{1}{2} y - 3}\) 1p ○ \(5 x = 7^{\frac{1}{2} y - 3} + 4\) \(x = \frac{1}{5} ⋅ 7^{\frac{1}{2} y - 3} + \frac{4}{5}\) 1p

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