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 \(y = 900 x^{1{,}98}\) in de vorm \(\log(y) = a + b ⋅ \log(x) \text{.}\) Geef \(a\) in twee decimalen.	○ \(y = 900 x^{1{,}98}\) \(\log(y) = \log(900 x^{1{,}98})\) 1p ○ \(\log(y) = \log(900) + \log(x^{1{,}98})\) \(\log(y) = \log(900) + 1{,}98 ⋅ \log(x)\) 1p ○ \(\log(y) = 2{,}954... + 1{,}98 ⋅ \log(x)\) Dus \(y = 2{,}95 + 1{,}98 ⋅ \log(x) \text{.}\) 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 \(y = {70 \over x^{3} \sqrt{x}}\) in de vorm \(\log(y) = a + b ⋅ \log(x) \text{.}\) Geef \(a\) in twee decimalen.	○ \(y = {70 \over x^{3} \sqrt{x}} = 70 x^{-3{,}5}\) \(\log(y) = \log(70 x^{-3{,}5})\) 1p ○ \(\log(y) = \log(70) + \log(x^{-3{,}5})\) \(\log(y) = \log(70) - 3{,}5 ⋅ \log(x)\) 1p ○ \(\log(y) = 1{,}845... - 3{,}5 ⋅ \log(x)\) Dus \(y = 1{,}85 - 3{,}5 ⋅ \log(x) \text{.}\) 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 \(\log(y) = 1{,}53 + 1{,}98 ⋅ \log(x)\) in de vorm \(y = a x^{b} \text{.}\) Geef \(a\) in gehelen.	○ \(\log(y) = 1{,}53 + 1{,}98 ⋅ \log(x)\) \(\log(y) = \log(10^{1{,}53}) + \log(x^{1{,}98})\) \(\log(y) = \log(10^{1{,}53} ⋅ x^{1{,}98})\) 1p ○ \(y = 10^{1{,}53} ⋅ x^{1{,}98}\) 1p ○ \(y = 33{,}884... ⋅ x^{1{,}98}\) Dus \(y = 34 ⋅ x^{1{,}98} \text{.}\) 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 \(y = 9\,400 ⋅ 1{,}21^{x}\) in de vorm \(\log(y) = a x + b \text{.}\) Geef \(a\) in vier decimalen en \(b\) in twee decimalen.	○ \(y = 9\,400 ⋅ 1{,}21^{x}\) \(\log(y) = \log(9\,400 ⋅ 1{,}21^{x})\) \(\log(y) = \log(9\,400) + \log(1{,}21^{x})\) 1p ○ \(\log(y) = \log(9\,400) + x ⋅ \log(1{,}21)\) 1p ○ \(\log(y) = 3{,}973... + x ⋅ 0{,}08278...\) Dus \(\log(y) = 0{,}0828 x + 3{,}97\) 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 \(y = 3\,900 ⋅ 1{,}24^{5 x + 3}\) in de vorm \(\log(y) = a x + b \text{.}\) Geef \(a\) in vier decimalen en \(b\) in twee decimalen.	○ \(y = 3\,900 ⋅ 1{,}24^{5 x + 3}\) \(\log(y) = \log(3\,900 ⋅ 1{,}24^{5 x + 3})\) \(\log(y) = \log(3\,900) + \log(1{,}24^{5 x + 3})\) 1p ○ \(\log(y) = \log(3\,900) + (5 x + 3) ⋅ \log(1{,}24)\) \(\log(y) = \log(3\,900) + 5 x ⋅ \log(1{,}24) + 3 ⋅ \log(1{,}24)\) 1p ○ \(\log(y) = 3{,}591... + 5 x ⋅ 0{,}09342... + 3 ⋅ 0{,}09342...\) \(\log(y) = 3{,}591... + 0{,}46710... ⋅ x + 0{,}28026...\) Dus \(\log(y) = 0{,}4671 x + 3{,}87\) 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 \(\log(y) = 0{,}5688 x + 1{,}28\) in de vorm \(y = b ⋅ g^{x} \text{.}\) Geef \(b\) in gehelen en \(g\) in twee decimalen.	○ \(\log(y) = 0{,}5688 x + 1{,}28\) \(y = 10^{0{,}5688 x + 1{,}28}\) 1p ○ \(y = 10^{0{,}5688 x} ⋅ 10^{1{,}28}\) \(y = (10^{0{,}5688})^{x} ⋅ 10^{1{,}28}\) 1p ○ \(y = 3{,}705...^{x} ⋅ 19{,}054...\) Dus \(y = 19 ⋅ 3{,}71^{x} \text{.}\) 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 \(y = 3{,}23 ⋅ {}^{5}\!\log(x) + 1{,}47\) in de vorm \(y = {}^{5}\!\log(a x^{b}) \text{.}\) Geef \(a\) en \(b\) in twee decimalen.	○ \(y = 3{,}23 ⋅ {}^{5}\!\log(x) + 1{,}47\) \(\text{ } = {}^{5}\!\log(x^{3{,}23}) + 1{,}47\) 1p ○ \(\text{ } = {}^{5}\!\log(x^{3{,}23}) + {}^{5}\!\log(5^{1{,}47})\) \(\text{ } = {}^{5}\!\log(x^{3{,}23} ⋅ 5^{1{,}47})\) 1p ○ \(\text{ } = {}^{5}\!\log(x^{3{,}23} ⋅ 10{,}653...)\) Dus \(y = {}^{5}\!\log(10{,}65 ⋅ x^{3{,}23}) \text{.}\) 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 \(y = {}^{3}\!\log(1{,}1 x) - 1{,}4\) in de vorm \(y = a + b ⋅ {}^{2}\!\log(x) \text{.}\) Geef \(a\) en \(b\) in twee decimalen.	○ \(y = {}^{3}\!\log(1{,}1 x) - 1{,}4\) \(\text{ } = {}^{3}\!\log(1{,}1) + {}^{3}\!\log(x) - 1{,}4\) 1p ○ \(\text{ } = {}^{3}\!\log(1{,}1) - 1{,}4 + {{}^{2}\!\log(x) \over {}^{2}\!\log(3)}\) \(\text{ } = {}^{3}\!\log(1{,}1) - 1{,}4 + {1 \over {}^{2}\!\log(3)} ⋅ {}^{2}\!\log(x)\) 1p ○ \(\text{ } = 0{,}086... - 1{,}4 + {1 \over 1{,}584...} ⋅ {}^{2}\!\log(x)\) \(\text{ } = -1{,}313... + 0{,}630... ⋅ {}^{2}\!\log(x)\) Dus \(y = -1{,}31 + 0{,}63 ⋅ {}^{2}\!\log(x) \text{.}\) 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 \(y = 7 ⋅ {}^{2}\!\log(32 x) + 6\) in de vorm \(y = a + b ⋅ {}^{2}\!\log(4 x) \text{.}\)	○ \(y = 7 ⋅ {}^{2}\!\log(32 x) + 6\) \(\text{ } = 7 ⋅ ({}^{2}\!\log(8) + {}^{2}\!\log(4 x)) + 6\) 1p ○ \(\text{ } = 7 ⋅ (3 + {}^{2}\!\log(4 x)) + 6\) 1p ○ \(\text{ } = 21 + 7 ⋅ {}^{2}\!\log(4 x) + 6\) \(\text{ } = 27 + 7 ⋅ {}^{2}\!\log(4 x)\) 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 \(y = {}^{5}\!\log({100 \over x^{3} \sqrt{x}})\) in de vorm \(y = a + b ⋅ {}^{5}\!\log(x) \text{.}\) Geef \(a\) in twee decimalen.	○ \(y = {}^{5}\!\log({100 \over x^{3} \sqrt{x}})\) \(\text{ } = {}^{5}\!\log(100 x^{-3{,}5})\) 1p ○ \(\text{ } = {}^{5}\!\log(100) + {}^{5}\!\log(x^{-3{,}5})\) \(\text{ } = {}^{5}\!\log(100) - 3{,}5 ⋅ {}^{5}\!\log(x)\) 1p ○ \(\text{ } = 2{,}861... - 3{,}5 ⋅ {}^{5}\!\log(x)\) Dus \(y = 2{,}86 - 3{,}5 ⋅ {}^{5}\!\log(x) \text{.}\) 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 \(y = 4 + 4 ⋅ {}^{3}\!\log(8 x - 6)\)	○ \(y = 4 + 4 ⋅ {}^{3}\!\log(8 x - 6)\) \(4 ⋅ {}^{3}\!\log(8 x - 6) = y - 4\) \({}^{3}\!\log(8 x - 6) = \frac{1}{4} y - 1\) 1p ○ \(8 x - 6 = 3^{\frac{1}{4} y - 1}\) 1p ○ \(8 x = 3^{\frac{1}{4} y - 1} + 6\) \(x = \frac{1}{8} ⋅ 3^{\frac{1}{4} y - 1} + \frac{3}{4}\) 1p

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