Formules in de gevraagde vorm schrijven

20 - 12 oefeningen

DubbelLogaritmisch (1) 00ks - basis - dynamic variables	Getal & Ruimte (12e editie) - havo wiskunde B - 9.4
3p a Schrijf de formule \(y=270x^{1{,}11}\) in de vorm \(\log(y)=a+b⋅\log(x)\text{.}\) Geef \(a\) in twee decimalen.	a \(y=270x^{1{,}11}\) \(\log(y)=\log(270x^{1{,}11})\) 1p \(\log(y)=\log(270)+\log(x^{1{,}11})\) \(\log(y)=\log(270)+1{,}11⋅\log(x)\) 1p \(\log(y)=2{,}431...+1{,}11⋅\log(x)\) Dus \(y=2{,}43+1{,}11⋅\log(x)\text{.}\) 1p
DubbelLogaritmisch (2) 00kt - basis - dynamic variables	Getal & Ruimte (12e editie) - havo wiskunde B - 9.4
3p a Schrijf de formule \(y={570 \over x^3\sqrt{x}}\) in de vorm \(\log(y)=a+b⋅\log(x)\text{.}\) Geef \(a\) in twee decimalen.	a \(y={570 \over x^3\sqrt{x}}=570x^{-3{,}5}\) \(\log(y)=\log(570x^{-3{,}5})\) 1p \(\log(y)=\log(570)+\log(x^{-3{,}5})\) \(\log(y)=\log(570)-3{,}5⋅\log(x)\) 1p \(\log(y)=2{,}755...-3{,}5⋅\log(x)\) Dus \(y=2{,}76-3{,}5⋅\log(x)\text{.}\) 1p
DubbelLogaritmisch (3) 00kr - basis - dynamic variables	Getal & Ruimte (12e editie) - havo wiskunde B - 9.4
3p a Schrijf de formule \(\log(y)=1{,}34-1{,}82⋅\log(x)\) in de vorm \(y=ax^b\text{.}\) Geef \(a\) in gehelen.	a \(\log(y)=1{,}34-1{,}82⋅\log(x)\) \(\log(y)=\log(10^{1{,}34})+\log(x^{-1{,}82})\) \(\log(y)=\log(10^{1{,}34}⋅x^{-1{,}82})\) 1p \(y=10^{1{,}34}⋅x^{-1{,}82}\) 1p \(y=21{,}877...⋅x^{-1{,}82}\) Dus \(y=22⋅x^{-1{,}82}\text{.}\) 1p
Exponentieel (1) 00k8 - basis - dynamic variables	Getal & Ruimte (12e editie) - havo wiskunde A - 9.1
2p a Schrijf de formule \(y={532 \over 18{,}5⋅1{,}39^x}\) in de vorm \(y=b⋅g^x\text{.}\) Rond \(b\) af op één decimaal en \(g\) op 3 decimalen.	a \(y={532 \over 18{,}5⋅1{,}39^x}={532 \over 18{,}5}⋅{1 \over 1{,}39^x}={532 \over 18{,}5}⋅1{,}39^{-x}={532 \over 18{,}5}⋅(1{,}39^{-1})^x\) 1p \(y={532 \over 18{,}5}⋅(1{,}39^{-1})^x=28{,}756...⋅0{,}7194...^x≈28{,}8⋅0{,}719^x\) 1p
Exponentieel (2) 00k9 - basis - dynamic variables	Getal & Ruimte (12e editie) - havo wiskunde A - 9.1
2p a Schrijf de formule \(y={782⋅1{,}38^x \over 49⋅0{,}79^x}\) in de vorm \(y=b⋅g^x\text{.}\) Rond \(b\) af op één decimaal en \(g\) op 3 decimalen.	a \(y={782⋅1{,}38^x \over 49⋅0{,}79^x}={782 \over 49}⋅{1{,}38^x \over 0{,}79^x}={782 \over 49}⋅({1{,}38 \over 0{,}79})^x\) 1p \(y={782 \over 49}⋅({1{,}38 \over 0{,}79})^x=15{,}959...⋅1{,}7468...^x≈16{,}0⋅1{,}747^x\) 1p
Logaritmisch (1) 00ko - basis - dynamic variables	Getal & Ruimte (12e editie) - havo wiskunde B - 9.4
3p a Schrijf de formule \(y=4\,300⋅0{,}79^x\) in de vorm \(\log(y)=ax+b\text{.}\) Geef \(a\) in vier decimalen en \(b\) in twee decimalen.	a \(y=4\,300⋅0{,}79^x\) \(\log(y)=\log(4\,300⋅0{,}79^x)\) \(\log(y)=\log(4\,300)+\log(0{,}79^x)\) 1p \(\log(y)=\log(4\,300)+x⋅\log(0{,}79)\) 1p \(\log(y)=3{,}633...+x⋅-0{,}10237...\) Dus \(\log(y)=-0{,}1024x+3{,}63\) 1p
Logaritmisch (2) 00kp - basis - dynamic variables	Getal & Ruimte (12e editie) - havo wiskunde B - 9.4
3p a Schrijf de formule \(y=3\,800⋅0{,}92^{5x+1}\) in de vorm \(\log(y)=ax+b\text{.}\) Geef \(a\) in vier decimalen en \(b\) in twee decimalen.	a \(y=3\,800⋅0{,}92^{5x+1}\) \(\log(y)=\log(3\,800⋅0{,}92^{5x+1})\) \(\log(y)=\log(3\,800)+\log(0{,}92^{5x+1})\) 1p \(\log(y)=\log(3\,800)+(5x+1)⋅\log(0{,}92)\) \(\log(y)=\log(3\,800)+5x⋅\log(0{,}92)+1⋅\log(0{,}92)\) 1p \(\log(y)=3{,}579...+5x⋅-0{,}03621...+1⋅-0{,}03621...\) \(\log(y)=3{,}579...-0{,}18106...⋅x-0{,}03621...\) Dus \(\log(y)=-0{,}1811x+3{,}54\) 1p
Logaritmisch (3) 00kq - basis - dynamic variables	Getal & Ruimte (12e editie) - havo wiskunde B - 9.4
3p a Schrijf de formule \(\log(y)=0{,}7508x+1{,}84\) in de vorm \(y=b⋅g^x\text{.}\) Geef \(b\) in gehelen en \(g\) in twee decimalen.	a \(\log(y)=0{,}7508x+1{,}84\) \(y=10^{0{,}7508x+1{,}84}\) 1p \(y=10^{0{,}7508x}⋅10^{1{,}84}\) \(y=(10^{0{,}7508})^x⋅10^{1{,}84}\) 1p \(y=5{,}633...^x⋅69{,}183...\) Dus \(y=69⋅5{,}63^x\text{.}\) 1p
Logaritmisch (4) 00l0 - basis - dynamic variables	Getal & Ruimte (12e editie) - havo wiskunde B - 9.3
3p a Schrijf de formule \(y=1{,}13⋅{}^{5}\!\log(x)-1{,}51\) in de vorm \(y={}^{5}\!\log(ax^b)\text{.}\) Geef \(a\) en \(b\) in twee decimalen.	a \(y=1{,}13⋅{}^{5}\!\log(x)-1{,}51\) \(\text{ }={}^{5}\!\log(x^{1{,}13})-1{,}51\) 1p \(\text{ }={}^{5}\!\log(x^{1{,}13})+{}^{5}\!\log(5^{-1{,}51})\) \(\text{ }={}^{5}\!\log(x^{1{,}13}⋅5^{-1{,}51})\) 1p \(\text{ }={}^{5}\!\log(x^{1{,}13}⋅0{,}088...)\) Dus \(y={}^{5}\!\log(0{,}09⋅x^{1{,}13})\text{.}\) 1p
Logaritmisch (5) 00l1 - basis - dynamic variables	Getal & Ruimte (12e editie) - havo wiskunde B - 9.3
3p a Schrijf de formule \(y={}^{2}\!\log({46 \over x^4})\) in de vorm \(y=a+b⋅{}^{2}\!\log(x)\text{.}\) Geef \(a\) in twee decimalen.	a \(y={}^{2}\!\log({46 \over x^4})\) \(\text{ }={}^{2}\!\log(46x^{-4})\) 1p \(\text{ }={}^{2}\!\log(46)+{}^{2}\!\log(x^{-4})\) \(\text{ }={}^{2}\!\log(46)-4⋅{}^{2}\!\log(x)\) 1p \(\text{ }=5{,}523...-4⋅{}^{2}\!\log(x)\) Dus \(y=5{,}52-4⋅{}^{2}\!\log(x)\text{.}\) 1p
Logaritmisch (6) 00l2 - basis - dynamic variables	Getal & Ruimte (12e editie) - havo wiskunde B - 9.3
3p a Schrijf de formule \(y={}^{3}\!\log(1{,}7x)-0{,}5\) in de vorm \(y=a+b⋅{}^{2}\!\log(x)\text{.}\) Geef \(a\) en \(b\) in twee decimalen.	a \(y={}^{3}\!\log(1{,}7x)-0{,}5\) \(\text{ }={}^{3}\!\log(1{,}7)+{}^{3}\!\log(x)-0{,}5\) 1p \(\text{ }={}^{3}\!\log(1{,}7)-0{,}5+{{}^{2}\!\log(x) \over {}^{2}\!\log(3)}\) \(\text{ }={}^{3}\!\log(1{,}7)-0{,}5+{1 \over {}^{2}\!\log(3)}⋅{}^{2}\!\log(x)\) 1p \(\text{ }=0{,}482...-0{,}5+{1 \over 1{,}584...}⋅{}^{2}\!\log(x)\) \(\text{ }=-0{,}017...+0{,}630...⋅{}^{2}\!\log(x)\) Dus \(y=-0{,}02+0{,}63⋅{}^{2}\!\log(x)\text{.}\) 1p
Logaritmisch (7) 00l3 - basis - dynamic variables	Getal & Ruimte (12e editie) - havo wiskunde B - 9.3
3p a Schrijf de formule \(y=8⋅{}^{4}\!\log(48x)+5\) in de vorm \(y=a+b⋅{}^{4}\!\log(3x)\text{.}\)	a \(y=8⋅{}^{4}\!\log(48x)+5\) \(\text{ }=8⋅({}^{4}\!\log(16)+{}^{4}\!\log(3x))+5\) 1p \(\text{ }=8⋅(2+{}^{4}\!\log(3x))+5\) 1p \(\text{ }=16+8⋅{}^{4}\!\log(3x)+5\) \(\text{ }=21+8⋅{}^{4}\!\log(3x)\) 1p

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