Herleiden m.b.v. de rekenregels voor logaritmen

Leerdoelen

•Je kunt de rekenregels voor logaritmen benoemen.

•Je kunt logaritmische formules herleiden met behulp van de rekenregels.

Welke rekenregels voor logaritmen zijn er?

Er zijn zes belangrijke rekenregels voor logaritmen die helpen bij het herleiden van uitdrukkingen. Deze regels beschrijven hoe logaritmen met hetzelfde grondtal (het kleine getal rechtsonder de 'log') bij elkaar opgeteld, afgetrokken of omgezet kunnen worden. Herleiden is het omzetten van een logaritmische uitdrukking of formule naar een andere, equivalente vorm.

De zes rekenregels voor logaritmen zijn:

Hoe herken je de tien log?

Als er bij een logaritme geen grondtal staat, zoals 'log T', dan betreft het de tienlog → ^{10}\log\left(x\right)^{10}\log\left(x\right)\log_{\placeholder{}}^{10}\log\left(x\right)lo^{10}\log\left(x\right)l^{10}\log\left(x\right)^{10}\log\left(x\right)\log^{10}\log\left(x\right)\log d^{10}\log\left(x\right)\log dc^{10}\log\left(x\right)\log dc^{10}\log\left(x\right)\log^{10}\log\left(x\right)^{10}\log\left(x\right)^{10}\log\left(\right)^{10}\log^{10}^{10\log}^{10}^1^19^1. Dit is een logaritme met grondtal 10. Dit grondtal wordt dan niet geschreven, maar moet wel in gedachten worden gehouden bij het herleiden.

Hoe breng je een factor of constante in de logaritme?

Een factor die voor een logaritme staat, kan in de logaritme worden gebracht met behulp van rekenregel 3. Een constante zonder logaritme kan worden omgezet naar een logaritme met een gewenst grondtal door gebruik te maken van rekenregel 6.

Rekenvoorbeeld: Herleid de formule N=2,5\cdot^{10}\log\left(t\right)-5N=2,5\cdot^{10}\log\left(t\right)-N=2,5\cdot^{10}\log\left(t\right)N=2,5\cdot^{10}\log\left(t\right)N=2,5\cdot^{10}\log\left(\right)N=2,5\cdot^{10}\logN=2,5\cdot^{10}N=2,5\cdot^1N=2,5\cdot^{1^{}}N=2,5\cdot^{1^0}N=2,5\cdot^{1^{}}N=2,5\cdot^{1^{-}}N=2,5\cdot^1N=2,5\cdot^10N=2,5\cdot^1N=2,5\cdot^{}N=2,5\cdot^{^{}}N=2,5\cdot^{^1}N=2,5\cdot^{^10}N=2,5\cdot^{^1}N=2,5\cdotN=2,5N=2,5lN=2,5loN=2,5logN=2,5logTN=2,5logT- naar de vorm N=^{10}\log\left(at^{b}\right)N=^{10}\log\left(at^{b}\right)N=^{10}\log\left(at^{}\right)N=^{10}\log\left(at^{^{}}\right)N=^{10}\log\left(at^{^{b}}\right)N=^{10}\log\left(at\right)N=^{10}\log\left(a\right)N=^{10}\log\left(\right)N=^{10}\logN=^{10}N=^1N=^10N=^1N=N=lN=loN=logN=log(N=log(AN=log(ATN=log(AT^{}N=log(AT^{B}.

N=2{,}5\cdot\log\left(t\right)-5N=2{,}5\cdot\log\left(t\right)-N=2{,}5\cdot\log\left(t\right)N=2{,}5\cdot\log\left(t\right)N=2{,}5\cdot\log\left(\right)N=2{,}5\cdot\logN=2{,}5\logN=2{,}5N=2{,}N=2N=

•Pas regel 3 toe op2{,}5\cdot\log\left(t\right)2{,}5\cdot\log\left(t\right)2{,}5\cdot\log\left(\right)2{,}5\cdot\log2{,}5\cdot25\cdot2.5\cdot2.5\cdot T2.5\cdot lT2.5\cdot loT2.5\cdot logT: de factor 2,5 wordt de exponent van T. N=\log(t^{2{,}5})-5N=\log(t^{2{,}})-5N=\log(t^2)-5N=\log(t^2.)-5N=\log(t^2.5)-5N=\log(^2.5)-5N=\log(T^2.5)-5N=(T^2.5)-5N=log(T^2.5)-5N=log(T^2.5)-5N=log(T^2.5)-5N=log(T^2.5)-5N=log(T^2.5)-5

•Zet de constante 5 om in een 10 log. Gebruik regel 6: ^{g}\log\left(g^{a}\right)=a. Hierbij is en . N=\log(t^{2{,}5})-\log(10^5)N=\log(t^{2{,}5})-(10^5)N=\log(t^{2{,}5})-l(10^5)N=\log(t^{2{,}5})-lo(10^5)N=\log(t^{2{,}5})-log(10^5)N=\log(^{2{,}5})-log(10^5)N=\log(T^{2{,}5})-log(10^5)N=\log(T^{2{,}})-log(10^5)N=\log(T^2)-log(10^5)N=\log(T^2.5)-log(10^5)N=(T^2.5)-log(10^5)N=l(T^2.5)-log(10^5)N=lo(T^2.5)-log(10^5) N=\log(t^{2{,}5})-\log(100.000)N=\log(^{2{,}5})-\log(100.000)N=\log(T^{2{,}5})-\log(100.000)N=\log(T^{2{,}5})-(100.000)N=\log(T^{2{,}5})-l(100.000)N=\log(T^{2{,}5})-lo(100.000)N=\log(T^{2{,}5})-log(100.000)N=\log(T^{2{,}})-log(100.000)N=\log(T^2)-log(100.000)N=\log(T^2.)-log(100.000)N=\log(T^2.5)-log(100.000)N=(T^2.5)-log(100.000)N=l(T^2.5)-log(100.000)N=lo(T^2.5)-log(100.000)

•Pas regel 2 toe: het verschil van twee logaritmen met hetzelfde grondtal (10) wordt de logaritme van het quotiënt. N=\log(\frac{t^{2{,}5}}{100.000})N=\log(\frac{^{2{,}5}}{100.000})N=\log(\frac{T^{2{,}5}}{100.000})N=(\frac{T^{2{,}5}}{100.000})N=l(\frac{T^{2{,}5}}{100.000})N=lo(\frac{T^{2{,}5}}{100.000})N=log(\frac{T^{2{,}5}}{100.000})N=log(\frac{T^{2{,}5}}{100.000}100.000)N=log(\frac{T^{2{,}5}}{100.00}100.000)N=log(\frac{T^{2{,}5}}{100.0}100.000)N=log(\frac{T^{2{,}5}}{100.}100.000)N=log(\frac{T^{2{,}5}}{100}100.000)N=log(\frac{T^{2{,}5}}{10}100.000)N=log(\frac{T^{2{,}5}}{1}100.000)N=log(\frac{T^{2{,}5}}{1-}100.000)N=log(\frac{T^{2{,}5}}{1--}100.000)N=log(\frac{T^{2{,}5}}{1-}100.000)N=log(\frac{T^{2{,}5}}{1}100.000)N=log(\frac{T^{2{,}5}}{\placeholder{}}100.000)N=log(T^{2{,}5}100.000)N=log(T^{2{,}5}/100.000)N=log(T^{2{,}}/100.000)N=log(T^2/100.000)N=log(T^2./100.000)

•Dit kan ook geschreven worden als: N=\log(\frac{1}{100.000}\cdot t^{2{,}5})N=\log(\frac{1}{100.000}\cdot t^{2{,}})N=\log(\frac{1}{100.000}\cdot t^2)N=\log(\frac{1}{100.000}\cdot t^2.)N=\log(\frac{1}{100.000}\cdot t^2.5)N=\log(\frac{1}{100.000}\cdot^2.5)N=\log(\frac{1}{100.000}\cdot5^2.5)N=\log(\frac{1}{100.000}\cdot^2.5)N=\log(\frac{1}{100.000}\cdot T^2.5)N=\log(\frac{1}{100.000}T^2.5)N=\log(\frac{1}{100.000}*T^2.5)N=\log(\frac{1}{100.00}*T^2.5)N=\log(\frac{1}{100.0}*T^2.5)N=\log(\frac{1}{100.}*T^2.5)N=\log(\frac{1}{100}*T^2.5)N=\log(\frac{1}{10}*T^2.5)N=\log(\frac11*T^2.5)N=\log(\frac{1}{\placeholder{}}*T^2.5)N=\log(1*T^2.5)N=\log(1/*T^2.5)N=\log(1/1*T^2.5)N=\log(1/10*T^2.5)N=\log(1/100*T^2.5)N=\log(1/100.*T^2.5)N=\log(1/100.0*T^2.5)N=\log(1/100.00*T^2.5)N=\log(1/100.000*T^2.5)N=(1/100.000*T^2.5) N=\log(0.00001\cdot t^{2{,}5})N=(0.00001\cdot t^{2{,}5})N=l(0.00001\cdot t^{2{,}5})N=lo(0.00001\cdot t^{2{,}5})N=log(0.00001\cdot t^{2{,}5})N=log(0.00001\cdot^{2{,}5})N=log(0.00001^{2{,}5})N=log(0.00001T^{2{,}5})N=log(0.00001\cdot T^{2{,}5})N=log(0.00001\cdot T^{2{,}})N=log(0.00001\cdot T^2)N=log(0.00001\cdot T^2.)N=log(0.00001\cdot T^2.5)N=log(0.00001T^2.5) De formule is nu herleid naar de gewenste vorm N=^{10}\log\left(at^{b}\right), waarbij a=0{,}00001a=000001a=0.00001=0.00001 en b=2{,}5b=25b=2.5=2.5.

Hoe splits je een logaritme op?

Een logaritme met een product in het argument kan worden gesplitst in een som van twee logaritmen, door rekenregel 1 van rechts naar links toe te passen. Een logaritme met een quotiënt in het argument kan worden gesplitst in een verschil van twee logaritmen, door rekenregel 2 van rechts naar links toe te passen.

Belangrijk aandachtspunt: Bij het splitsen van logaritmen of het naar buiten halen van exponenten (regel 3 omgekeerd), moet je controleren of de exponent op de hele term of slechts een deel van de term staat.

Rekenvoorbeeld: Herleid de formule N=^3\log(81t^5)N=^3\log(81^5)N=^3\log(81T^5)N=^3(81T^5)N=^{}(81T^5)N=^2(81T^5)N=(81T^5)N=3(81T^5)N=3l(81T^5)N=3lo(81T^5) naar de vorm p+q\cdot^3\log\left(t\right)p+\cdot^3\log\left(t\right)p+Q\cdot^3\log\left(t\right)+Q\cdot^3\log\left(t\right)P+Q\cdot^3\log\left(t\right)P+Q\cdot^3\log\left(t\right)P+Q\cdot^3\log\left(\right)P+Q\cdot^3\logP+Q\cdot^3P+Q\cdotP+Q\cdot3P+Q\cdot3lP+Q\cdot3loP+Q\cdot3logP+Q\cdot3logTP+Q3logTP+Qk3logTP+Qke3logTP+Qkee3logT.

N=^3\log(81t^5)N=^3\log(81^5)N=^3\log(81T^5)N=^3(81T^5)N=^3l(81T^5)N=^3lo(81T^5)N=^3log(81T^5)N=log(81T^5)

•Let op: de exponent 5 staat alleen bij , niet bij 81.

•Splits het product 81\cdot t^581\cdot^581^581*^5 in de logaritme met regel 1. N=^3\log\left(81\right)+^3\log(t^5)N=^3\log\left(81+^3\log(t^5)\right)N=^3\log81+^3\log(t^5)N=^3\log81+^3\log(^5)N=^3\log81+^3\log(T^5)N=^3\log81+^3(T^5)N=^3\log81+(T^5)N=^3\log81+3(T^5)N=^3\log81+3l(T^5)N=^3\log81+3lo(T^5)N=^3\log81+3log(T^5)N=^381+3log(T^5)N=81+3log(T^5)N=381+3log(T^5)N=3l81+3log(T^5)N=3lo81+3log(T^5)

•Bereken de ^3\log\left(81\right). Omdat 81 = 3⁴ →^3\log\left(81\right)=4^3\log\left(81\right)=^3\log\left(81\right)^3\log\left(81\right)^3\log81^381813813l813lo81. N=4+^3\log(t^5)N=4+^3\log(^5)N=4+^3\log(T^5)N=4+^3(T^5)N=4+^3l(T^5)N=4+^3lo(T^5)N=4+^3log(T^5)N=4+log(T^5)

•Haal de exponent 5 voor de logaritme met regel 3. N=4+5\cdot^3\log\left(t\right)N=4+5\cdot^3\log\left(t\right)N=4+5\cdot^3\log\left(\right)N=4+5\cdot^3\logN=4+5\cdot^3\log TN=4+5\cdot^3TN=4+5\cdot^3lTN=4+5\cdot^3loTN=4+5\cdot^3logTN=4+5\cdot logTN=4+5\cdot3logTN=4+53logT De formule is nu herleid naar de gewenste vorm p+q\cdot^3\log\left(t\right), waarbij p=4=4 en q=5=5.

Hoe verander je het grondtal van een logaritme?

Het grondtal van een logaritme kan worden gewijzigd met rekenregel 4:^{g}\log\left(a\right)=\frac{^{p}\log\left(a\right)}{^{p}\log\left(g\right)}^{g}\log\left(a\right)=\frac{^{p}\log\left(a\right)}{^{p}\log\left(g\right)}/^{g}\log\left(a\right)=\frac{^{p}\log\left(a\right)}{^{p}\log\left(g\right)}/P^{g}\log\left(a\right)=\frac{^{p}\log\left(a\right)}{^{p}\log\left(g\right)}/Pl^{g}\log\left(a\right)=\frac{^{p}\log\left(a\right)}{^{p}\log\left(g\right)}/Pl^{g}\log\left(a\right)=\frac{^{p}\log\left(a\right)}{^{p}\log\left(g\right)}/Plo^{g}\log\left(a\right)=\frac{^{p}\log\left(a\right)}{^{p}\log\left(g\right)}/Plog^{g}\log\left(a\right)=\frac{^{p}\log\left(a\right)}{^{p}\log\left(g\right)}/PlogG^{g}\log\left(a\right)=\frac{^{p}\log\left(a\right)}{^{p}\log\left(g\right)}/PlogG^{g}\log\left(a\right)=\frac{^{p}\log\left(a\right)}{^{p}\log\left(\right)}/PlogG^{g}\log\left(a\right)=\frac{^{p}\log\left(a\right)}{^{p}\log}/PlogG^{g}\log\left(a\right)=\frac{^{p}\log\left(a\right)}{^{p}}/PlogG^{g}\log\left(a\right)=\frac{^{p}\log\left(a\right)}{}/PlogG^{g}\log\left(a\right)=\frac{^{p}\log\left(a\right)}{\placeholder{}}/PlogG^{g}\log\left(a\right)=\frac{^{p}\log\left(a\right)}{\placeholder{}^{}}/PlogG^{g}\log\left(a\right)=\frac{^{p}\log\left(a\right)}{\placeholder{}^{p}}/PlogG^{g}\log\left(a\right)=\frac{^{p}\log\left(a\right)}{\placeholder{}}/PlogG^{g}\log\left(a\right)=^{p}\log\left(a\right)/PlogG^{g}\log\left(a\right)=^{p}\log\left(a/PlogG\right)^{g}\log\left(a\right)=^{p}\log\left(/PlogG\right)^{g}\log\left(a\right)=^{p}\log/PlogG^{g}\log\left(a\right)=^{p}\log a/PlogG^{g}\log\left(a\right)=^{p}\log/PlogG^{g}\log\left(a\right)=^{p}/PlogG^{g}\log\left(a\right)=/PlogG^{g}\log\left(a\right)=\&/PlogG^{g}\log\left(a\right)=/PlogG^{g}\log\left(a\right)=P/PlogG^{g}\log\left(a\right)=Pl/PlogG^{g}\log\left(a\right)=Plo/PlogG^{g}\log\left(a\right)=Plog/PlogG^{g}\log\left(a\right)=PlogA/PlogG^{g}\log\left(a=PlogA/PlogG\right)^{g}\log\left(=PlogA/PlogG\right)^{g}\log=PlogA/PlogG^{g}=PlogA/PlogG^{g}l=PlogA/PlogG^{g}lo=PlogA/PlogG^{g}log=PlogA/PlogG^{g}logA=PlogA/PlogGlogA=PlogA/PlogG. Dit is handig als je naar een standaard grondtal (zoals 10) wilt herleiden.

Rekenvoorbeeld: Herleid de formule P=0{,}3+^2\log(6{,}4Q)P=03+^2\log(6{,}4Q)P=0.3+^2\log(6{,}4Q)P=0.3+^2\log(6{,}4)P=0.3+^2\log(6{,}4q)P=0.3+^2\log(64q)P=0.3+^2\log(6.4q)P=0.3+^2\log(6.4)P=0.3+^2\log(6.4g)P=0.3+^2\log(6.4)P=0.3+^2\log(6.4Q)P=0.3+^2(6.4Q)P=0.3+(6.4Q) naar de vorm P=a+b\cdot\log\left(Q\right)P=a+b\cdot\log\left(Q\right)P=a+b\cdot\log\left(\right)P=a+b\cdot\logP=a+b\cdotP=a+b\cdot lP=a+b\cdotP=a+bP=a+P=aP=PP=P=AP=A+P=A+BP=A+BkP=A+BkeP=A+BkeeP=A+BkeerP=A+BkeerlP=A+BkeerloP=A+Bkeerlog. Rond a en bBB af op twee decimalen.

P=0{,}3+^2\log(6{,}4Q)P=03+^2\log(6{,}4Q)P=0.3+^2\log(6{,}4Q)P=0.3+^2\log(64Q)P=0.3+^2\log(6.4Q)P=0.3+^2(6.4Q)P=0.3+(6.4Q)

•Splits het product 6{,}4\cdot Q64\cdot Q6.4\cdot Q6.4Q in de ^2\log^222l2lo met regel 1. P=0{,}3+^2\log\left(6{,}4\right)+^2\log\left(Q\right)P=03+^2\log\left(6{,}4\right)+^2\log\left(Q\right)P=0.3+^2\log\left(6{,}4\right)+^2\log\left(Q\right)P=0.3+^2\log\left(6{,}4\right)+^2\log\left(Q\right)P=0.3+^2\log\left(6{,}4\right)+^2\log\left(\right)P=0.3+^2\log\left(6{,}4\right)+^2\logP=0.3+^2\log\left(6{,}4\right)+^2P=0.3+^2\log\left(6{,}4\right)+P=0.3+^2\log\left(6{,}4\right)+2logQP=0.3+^2\log\left(6{,}4+2logQ\right)P=0.3+^2\log\left(6{,}+2logQ\right)P=0.3+^2\log\left(6+2logQ\right)P=0.3+^2\log\left(+2logQ\right)P=0.3+^2\log+2logQP=0.3+^2+2logQP=0.3++2logQ

•Bereken ^2\log\left(6{,}4\right)^2\log\left(6{,}4\right)^2\log\left(6{,}\right)^2\log\left(6\right)^2\log\left(\right)^2\log^2. Dit is ongeveer 2{,}6782678. P=0{,}3+2{,}678...+^2\log\left(Q\right)P=0{,}3+2678...+^2\log\left(Q\right)P=0{,}3+2.678...+^2\log\left(Q\right)P=03+2.678...+^2\log\left(Q\right)P=0.3+2.678...+^2\log\left(Q\right)P=0.3+2.678...+^2\log\left(Q\right)P=0.3+2.678...+^2\log\left(\right)P=0.3+2.678...+^2\logP=0.3+2.678...+^2P=0.3+2.678...+

•Tel de constanten op. P=2{,}978...+^2\log\left(Q\right)P=2978...+^2\log\left(Q\right)P=2.978...+^2\log\left(Q\right)P=2.978...+^2\log\left(Q\right)P=2.978...+^2\log\left(\right)P=2.978...+^2\logP=2.978...+^2P=2.978...+

•Verander het grondtal van ^2\log\left(Q\right)^2\log\left(Q\right)^2\log\left(\right)^2\log^222l2lo2log naar de ^{10}\log\left(x\right)^{10}\log\left(x^{}\right)^{10}\log\left(x^1\right)^{10}\log\left(x^{10}\right)^1\log\left(x^{10}\right)^10\log\left(x^{10}\right)^1\log\left(x^{10}\right)^{}\log\left(x^{10}\right)^{}\log\left(x^1\right)^{}\log\left(x^10\right)^{}\log\left(x^1\right)^{}\log\left(x\right)^{}\log\left(\right)^{}\log\left(1\right)^{}\log\left(10\right)^1\log\left(10\right)^{10}\log\left(10\right)^{10}\log\left(10\right)^{10}\log\left(1\right)^{10}\log\left(\right)^{10}\log^{10}^1^10^111010l10lo(gewoon 'log') met regel 4. Hierbij is g=2=2, p=10.=10. P=2{,}978...+\frac{\log\left(Q\right)}{\log\left(2\right)}P=2978...+\frac{\log\left(Q\right)}{\log\left(2\right)}P=2.978...+\frac{\log\left(Q\right)}{\log\left(2\right)}P=2.978...+(\frac{\log\left(Q\right)}{\log\left(2\right)}P=2.978...+(\frac{\log\left(Q\right)}{\log\left(2\right)}P=2.978...+(\frac{\log\left(Q\right)}{\log\left(\right)}P=2.978...+(\frac{\log\left(Q\right)}{\log}P=2.978...+(\frac{\log\left(Q\right)}{\placeholder{}}P=2.978...+(\log\left(Q\right)P=2.978...+(\log\left(Q\right)P=2.978...+(\log\left(Q/\right)P=2.978...+(\log\left(Q/l\right)P=2.978...+(\log\left(Q/lo\right)P=2.978...+(\log\left(Q/log\right)P=2.978...+(\log\left(Q/log2\right)P=2.978...+(\log\left(Q)/log2\right)P=2.978...+(\log\left(Q))/log2\right)P=2.978...+(\log\left(\frac{Q))}{\placeholder{}}/log2\right)P=2.978...+(\log\left(Q))/log2\right)P=2.978...+(\log\left(Q)/log2\right)P=2.978...+(\log\left(\frac{Q)}{\placeholder{}}/log2\right)P=2.978...+(\log\left(Q)/log2\right)P=2.978...+(\log\left(Q/log2\right)P=2.978...+(\log\left(/log2\right)PQ=2.978...+(\log\left(/log2\right)PQ)=2.978...+(\log\left(/log2\right)PQ=2.978...+(\log\left(/log2\right)P=2.978...+(\log\left(/log2\right)P=2.978...+(\log/log2)P=2.978...+(/log2)P=2.978...+(\log/log2)P=2.978...+(\log\left(/log2\right)PQ=2.978...+(\log\left(/log2\right)PQ=2.978...+(\log\left(/log2\right)PQ)=2.978...+(\log\left(/log2\right)PQ=2.978...+(\log\left(/log2\right)P=2.978...+(\log\left(/log2\right)P=2.978...+(\log/log2)P=2.978...+(/log2)P=2.978...+(l/log2)P=2.978...+(lo/log2)P=2.978...+(log/log2)

•Herschrijf \frac{\log\left(Q\right)}{\log2}\frac{\log\left(Q\right)}{\log2}\log2\frac{\log\left(Q\right)}{\placeholder{}}\log2\log\left(Q\right)\log2 als \frac{1}{\log\left(2\right)}\cdot\log\left(Q\right)\frac{1}{\log\left(2\right)}\cdot\log\left(Q\right)\frac{1}{\log\left(2\right)}\cdot\log\left(\right)\frac{1}{\log\left(2\right)}\cdot\log\frac{1}{\log\left(2\right)}\cdot\frac{1}{\log\left(2\right)}\frac{1}{\log\left(2\right)}\frac{1}{\log\left(\right)}\frac{1}{\log}\frac{1}{}\frac{1}{p}\frac{1}{\placeholder{}}111/1/l1/lo1/log. P=2{,}978...+\frac{1}{\log\left(2\right)}\cdot\log\left(Q\right)P=2978...+\frac{1}{\log\left(2\right)}\cdot\log\left(Q\right)P=2.978...+\frac{1}{\log\left(2\right)}\cdot\log\left(Q\right)P=2.978...+P=2.978...+(P=2.978...+(1P=2.978...+(1/P=2.978...+(1/lP=2.978...+(1/loP=2.978...+(1/logP=2.978...+(1/log2P=2.978...+(1/log2)P=2.978...+(1/log2)*P=2.978...+(1/log2)*lP=2.978...+(1/log2)*loP=2.978...+(1/log2)*log

•Bereken \frac{1}{\log2}\frac{1}{\log2}\log\frac{1}{\log2}\log2\frac{1}{\placeholder{}}\log21\log2. Dit is ongeveer 3{,}321933219. P=2{,}978...+3{,}3219...\cdot\log\left(Q\right)P=2{,}978...+33219...\cdot\log\left(Q\right)P=2{,}978...+3.3219...\cdot\log\left(Q\right)P=2978...+3.3219...\cdot\log\left(Q\right)P=2.978...+3.3219...\cdot\log\left(Q\right)P=2.978...+3.3219...\cdot\log\left(Q\right)P=2.978...+3.3219...\cdot\log\left(\right)P=2.978...+3.3219...\cdot\logP=2.978...+3.3219...\cdotP=2.978...+3.3219...\cdot lP=2.978...+3.3219...\cdot loP=2.978...+3.3219...\cdot logP=2.978...+3.3219...\cdot logQP=2.978...+3.3219...logQ

•Rond de constanten af op twee decimalen. P=2.98+3.32\cdot\log\left(Q\right)P=2.98+3.32\cdot\log\left(Q\right)P=2.98+3.32\cdot\log\left(\right)P=2.98+3.32\cdot\logP=2.98+3.32\cdotP=2.98+3.32P=2.98+3.32*P=2.98+3.32*lP=2.98+3.32*loP=2.98+3.32*log De formule is nu herleid naar de gewenste vorm P=a+b\cdot\log\left(Q\right), waarbij a=2.98=2.98 en b=3.32=3.32.

Rekenvoorbeeld: Herleid de formule P=0.3+^2\log(6{,}4Q)P=0.3+^2\log(64Q)P=0.3+^2\log(6.4Q)P=0.3+^2(6.4Q)P=0.3+(6.4Q)P=0.3+2(6.4Q)P=0.3+2l(6.4Q)P=0.3+2lo(6.4Q) naar de vorm P=\log(aQ^{B})P=(aQ^{B})P=l(aQ^{B})P=lo(aQ^{B})P=log(aQ^{B})P=log(Q^{B}). Rond a en b af op twee decimalen.

P=0{,}3+^2\log(6{,}4Q)P=0{,}3+^2\log(64Q)P=0{,}3+^2\log(6.4Q)P=03+^2\log(6.4Q)P=0.3+^2\log(6.4Q)P=0.3+^2(6.4Q)P=0.3+(6.4Q)P=0.3+2(6.4Q)

•Zet de constante om in een \log\left(10^{x}\right)\log\left(10\right)\log\left(10\right)\log\left(1\right)\log\left(\right)\log\left(2\right)\log\left(20\right)\log\left(2\right)\log\left(\right)\log (gewoon 'log') met regel 6. P=\log(10^{0{,}3})+^2\log(6{,}4Q)P=\log(10^{0{,}3})+^2\log(64Q)P=\log(10^{0{,}3})+^2\log(6.4Q)P=\log(10^{0{,}3})+^2(6.4Q)P=\log(10^{0{,}3})+^2l(6.4Q)P=\log(10^{0{,}3})+^2lg(6.4Q)P=\log(10^{0{,}3})+^2log(6.4Q)P=\log(10^{0{,}3})+log(6.4Q)P=\log(10^{0{,}3})+2log(6.4Q)P=\log(10^{0{,}})+2log(6.4Q)P=\log(10^0)+2log(6.4Q)P=\log(10^0.)+2log(6.4Q)P=\log(10^0.3)+2log(6.4Q)P=(10^0.3)+2log(6.4Q)P=l(10^0.3)+2log(6.4Q)P=lo(10^0.3)+2log(6.4Q)

•Verander het grondtal van ^2\log(6{,}4Q)^2\log(64Q)^2\log(6.4Q)^2(6.4Q)(6.4Q) naar de 10 log met regel 4. P=\log\left(10^{0{,}3}\right)\frac{\log(6{,}4Q)}{\log\left(2\right)}P=\log\left(10^{0{,}3}\right)\frac{\log(64Q)}{\log\left(2\right)}P=\log\left(10^{0{,}3}\right)\frac{\log(6.4Q)}{\log\left(2\right)}P=\log10^{0{,}3})\frac{\log(6.4Q)}{\log\left(2\right)}P=\log\left(10^{0{,}3})\frac{\log(6.4Q)}{\log\left(2\right)}\right.P=\log\left(10^{0{,}3})\frac{\log(6.4Q)}{\log\left(2\right)}l\right.P=\log\left(10^{0{,}3})\frac{\log(6.4Q)}{\log\left(2\right)}lo\right.P=\log\left(10^{0{,}3})\frac{\log(6.4Q)}{\log\left(2\right)}log\right.P=\log\left(10^{0{,}3})\frac{\log(6.4Q)}{\log\left(2\right)}log2\right.P=\log\left(10^{0{,}3})\frac{\log(6.4Q)}{\log\left(2\right)}log2\right)P=\log\left(10^{0{,}3}\frac{\log(6.4Q)}{\log\left(2\right)}log2\right)P=\log10^{0{,}3}\frac{\log(6.4Q)}{\log\left(2\right)}log2)P=10^{0{,}3}\frac{\log(6.4Q)}{\log\left(2\right)}log2)P=(10^{0{,}3}\frac{\log(6.4Q)}{\log\left(2\right)}log2)P=(10^{0{,}3})\frac{\log(6.4Q)}{\log\left(2\right)}log2)P=(10^{0{,}3})\frac{}{\placeholder{}}\frac{\log(6.4Q)}{\log\left(2\right)}log2)P=(10^{0{,}3})\frac{\frac{}{\placeholder{}}}{\placeholder{}}\frac{\log(6.4Q)}{\log\left(2\right)}log2)P=(10^{0{,}3})+\frac{\frac{}{\placeholder{}}}{\placeholder{}}\frac{\log(6.4Q)}{\log\left(2\right)}log2)P=(10^{0{,}3})+\frac{\frac{\frac{\placeholder{}}{\placeholder{}}}{\placeholder{}}}{\placeholder{}}\frac{\log(6.4Q)}{\log\left(2\right)}log2)P=(10^{0{,}3})+\frac{\frac{\placeholder{}}{\placeholder{}}}{\placeholder{}}\frac{\log(6.4Q)}{\log\left(2\right)}log2)P=(10^{0{,}3})+\frac{\placeholder{}}{\placeholder{}}\frac{\log(6.4Q)}{\log\left(2\right)}log2)P=(10^{0{,}3})+\frac{\log(6.4Q)}{\log\left(2\right)}log2)P=(10^{0{,}3})+(\frac{\log(6.4Q)}{\log\left(2\right)}log2)P=(10^{0{,}3})+(\frac{\log(6.4Q)}{\log\left(2\right)}log2)P=(10^{0{,}3})+(\frac{\log(6.4Q)}{\log\left(\right)}log2)P=(10^{0{,}3})+(\frac{\log(6.4Q)}{\log}log2)P=(10^{0{,}3})+(\frac{\log(6.4Q)}{\placeholder{}}log2)P=(10^{0{,}3})+(\log(6.4Q)log2)P=(10^{0{,}3})+(\log(6.4Q)/log2)P=(10^{0{,}3})+((6.4Q)/log2)P=(10^{0{,}3})+(l(6.4Q)/log2)P=(10^{0{,}3})+(lo(6.4Q)/log2)P=(10^{0{,}3})+(log(6.4Q)/log2)P=(10^{0{,}})+(log(6.4Q)/log2)P=(10^0)+(log(6.4Q)/log2)P=(10^0.)+(log(6.4Q)/log2)P=(10^0.3)+(log(6.4Q)/log2)P=l(10^0.3)+(log(6.4Q)/log2)P=lo(10^0.3)+(log(6.4Q)/log2)

•Bereken 10^{0{,}3}10^{0{,}}10^010^0. (ongeveer 1{,}9951995) en \frac{1}{\log\left(2\right)}\frac{1}{\log\left(2\right)}\frac{1}{\log\left(\right)}\frac{1}{\log}\frac{1}{\placeholder{}}11/1/l1/lo1/log (ongeveer 3{,}321933219). P=1{,}995...+3{,}3219...\cdot\log(6{,}4Q)P=1{,}995...+33219...\cdot\log(6{,}4Q)P=1{,}995...+3.3219...\cdot\log(6{,}4Q)P=1995...+3.3219...\cdot\log(6{,}4Q)P=1.995...+3.3219...\cdot\log(6{,}4Q)P=1.995...+3.3219...\cdot\log(64Q)P=1.995...+3.3219...\cdot\log(6.4Q)P=1.995...+3.3219...\cdot(6.4Q)P=1.995...+3.3219...\cdot l(6.4Q)P=1.995...+3.3219...\cdot lo(6.4Q)P=1.995...+3.3219...\cdot log(6.4Q)P=1.995...+3.3219...log(6.4Q)

•Breng de factor 3,3219... in de logaritme als exponent met regel 3. Let op de haakjes. P=\log(1{,}995...)+\log(\left(6{,}4Q\right)^{3{,}3219\ldots})P=\log(1{,}995...)+\log(\left(6{,}4Q\right)^{3{,}3219..})P=\log(1{,}995...)+\log(\left(6{,}4Q\right)^{3{,}3219.})P=\log(1{,}995...)+\log(\left(6{,}4Q\right)^{3{,}3219})P=\log(1995...)+\log(\left(6{,}4Q\right)^{3{,}3219})P=\log(1.995...)+\log(\left(6{,}4Q\right)^{3{,}3219})P=\log(1.995...)+\log(\left(6{,}4Q^{3{,}3219}\right))P=\log(1.995...)+\log((6{,}4Q)^{3{,}3219})P=\log(1.995...)+\log((6{,}4Q)^{3{,}3219}.)P=\log(1.995...)+\log((6{,}4Q)^{3{,}3219}.3)P=\log(1.995...)+\log((6{,}4Q)^{3{,}3219}.32)P=\log(1.995...)+\log((6{,}4Q)^{3{,}3219}.32.)P=\log(1.995...)+\log((6{,}4Q)^{3{,}3219}.32..)P=\log(1.995...)+\log((6{,}4Q)^{3{,}3219}.32...)P=\log(1.995...)+\log((6{,}4Q)^{3{,}3219}.321...)P=\log(1.995...)+\log((6{,}4Q)^{3{,}3219}.3219...)P=\log(1.995...)+\log((6{,}4Q)^{3{,}321}.3219...)P=\log(1.995...)+\log((6{,}4Q)^{3{,}32}.3219...)P=\log(1.995...)+\log((6{,}4Q)^{3{,}3}.3219...)P=\log(1.995...)+\log((6{,}4Q)^{3{,}}.3219...)P=\log(1.995...)+\log((6{,}4Q)^3.3219...)P=\log(1.995...)+\log((64Q)^3.3219...)P=\log(1.995...)+\log((6.4Q)^3.3219...)P=\log(1.995...)+((6.4Q)^3.3219...)P=\log(1.995...)+l((6.4Q)^3.3219...)P=\log(1.995...)+lo((6.4Q)^3.3219...)P=\log(1.995...)+log((6.4Q)^3.3219...)P=(1.995...)+log((6.4Q)^3.3219...)P=l(1.995...)+log((6.4Q)^3.3219...)P=lo(1.995...)+log((6.4Q)^3.3219...)

•Pas regel 1 toe: de som van twee logaritmen wordt de logaritme van het product.

•Werk de exponent uit: (6{,}4Q)^{3{,}3219\ldots}=6{,}4^{3.3219\ldots}\cdot Q^{3{,}3219\ldots}(6{,}4Q)^{3{,}3219\ldots}=6{,}4^{3.3219\ldots}\cdot Q^{3{,}3219..}(6{,}4Q)^{3{,}3219\ldots}=6{,}4^{3.3219\ldots}\cdot Q^{3{,}3219.}(6{,}4Q)^{3{,}3219\ldots}=6{,}4^{3.3219\ldots}\cdot Q^{3{,}3219}(6{,}4Q)^{3{,}3219\ldots}=6{,}4^{3.3219..}\cdot Q^{3{,}3219}(6{,}4Q)^{3{,}3219\ldots}=6{,}4^{3.3219.}\cdot Q^{3{,}3219}(6{,}4Q)^{3{,}3219\ldots}=6{,}4^{3.3219}\cdot Q^{3{,}3219}(6{,}4Q)^{3{,}3219\ldots}=64^{3.3219}\cdot Q^{3{,}3219}(6{,}4Q)^{3{,}3219\ldots}=6.4^{3.3219}\cdot Q^{3{,}3219}(64Q)^{3{,}3219\ldots}=6.4^{3.3219}\cdot Q^{3{,}3219}(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}\cdot Q^{3{,}3219}(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}\cdot Q^{3{,}3219}3(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}\cdot Q^{3{,}3219}32(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}\cdot Q^{3{,}3219}321(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}\cdot Q^{3{,}3219}3219(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}\cdot Q^{3{,}3219}3219.(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}\cdot Q^{3{,}3219}3219..(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}\cdot Q^{3{,}3219}3219...(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}\cdot Q^{3{,}321}3219...(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}\cdot Q^{3{,}32}3219...(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}\cdot Q^{3{,}3}3219...(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}\cdot Q^{3{,}}3219...(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}\cdot Q^33219...(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}\cdot Q^3.3219...(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}Q^3.3219...(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}*Q^3.3219...(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}.*Q^3.3219...(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}.3*Q^3.3219...(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}.3.*Q^3.3219...(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}.3..*Q^3.3219...(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}.3...*Q^3.3219...(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}.32...*Q^3.3219...(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}.321...*Q^3.3219...(6.4Q)^{3{,}3219\ldots}=6.4^{3.3219}.3219...*Q^3.3219...(6.4Q)^{3{,}3219\ldots}=6.4^{3.321}.3219...*Q^3.3219...(6.4Q)^{3{,}3219\ldots}=6.4^{3.32}.3219...*Q^3.3219...(6.4Q)^{3{,}3219\ldots}=6.4^{3.3}.3219...*Q^3.3219...(6.4Q)^{3{,}3219\ldots}=6.4^{3.}.3219...*Q^3.3219...(6.4Q)^{3{,}3219\ldots}=6.4^3.3219...*Q^3.3219...(6.4Q)^{3{,}3219\ldots}=6.4^3,.3219...*Q^3.3219...(6.4Q)^{3{,}3219\ldots}=6.4^3.3219...*Q^3.3219...(6.4Q)^{3{,}3219..}=6.4^3.3219...*Q^3.3219...(6.4Q)^{3{,}3219.}=6.4^3.3219...*Q^3.3219...(6.4Q)^{3{,}3219}=6.4^3.3219...*Q^3.3219...(6.4Q)^{3{,}3219}.=6.4^3.3219...*Q^3.3219...(6.4Q)^{3{,}3219}.3=6.4^3.3219...*Q^3.3219...(6.4Q)^{3{,}3219}.32=6.4^3.3219...*Q^3.3219...(6.4Q)^{3{,}3219}.321=6.4^3.3219...*Q^3.3219...(6.4Q)^{3{,}3219}.3219=6.4^3.3219...*Q^3.3219...(6.4Q)^{3{,}3219}.3219.=6.4^3.3219...*Q^3.3219...(6.4Q)^{3{,}3219}.3219..=6.4^3.3219...*Q^3.3219...(6.4Q)^{3{,}3219}.3219...=6.4^3.3219...*Q^3.3219...(6.4Q)^{3{,}321}.3219...=6.4^3.3219...*Q^3.3219...(6.4Q)^{3{,}32}.3219...=6.4^3.3219...*Q^3.3219...(6.4Q)^{3{,}3}.3219...=6.4^3.3219...*Q^3.3219...(6.4Q)^{3{,}}.3219...=6.4^3.3219...*Q^3.3219... P=\log(1{,}995...\cdot6{,}4^{3{,}3219\ldots}\cdot Q^{3{,}3219\ldots})P=\log(1{,}995...\cdot64^{3{,}3219\ldots}\cdot Q^{3{,}3219\ldots})P=\log(1{,}995...\cdot6.4^{3{,}3219\ldots}\cdot Q^{3{,}3219\ldots})P=\log(1995...\cdot6.4^{3{,}3219\ldots}\cdot Q^{3{,}3219\ldots})P=\log(1.995...\cdot6.4^{3{,}3219\ldots}\cdot Q^{3{,}3219\ldots})P=\log(1.995...\cdot6.4^{3{,}3219\ldots}\cdot Q^{3{,}3219\ldots}2)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}\cdot Q^{3{,}3219\ldots}21)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}\cdot Q^{3{,}3219\ldots}219)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}\cdot Q^{3{,}3219\ldots}219.)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}\cdot Q^{3{,}3219\ldots}219..)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}\cdot Q^{3{,}3219\ldots}219...)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}\cdot Q^{3{,}3219..}219...)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}\cdot Q^{3{,}3219.}219...)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}\cdot Q^{3{,}3219}219...)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}\cdot Q^{3{,}3219}.219...)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}\cdot Q^{3{,}3219}.3219...)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}\cdot Q^{3{,}321}.3219...)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}\cdot Q^{3{,}32}.3219...)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}\cdot Q^{3{,}3}.3219...)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}\cdot Q^{3{,}}.3219...)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}\cdot Q^3.3219...)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}Q^3.3219...)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}*Q^3.3219...)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}.*Q^3.3219...)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}.3*Q^3.3219...)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}.3.*Q^3.3219...)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}.3..*Q^3.3219...)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}.32..*Q^3.3219...)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}.321..*Q^3.3219...)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}.3219..*Q^3.3219...)P=\log(1.995...\cdot6.4^{3{,}3219\ldots}.3219...*Q^3.3219...)P=\log(1.995...\cdot6.4^{3{,}3219..}.3219...*Q^3.3219...)P=\log(1.995...\cdot6.4^{3{,}3219.}.3219...*Q^3.3219...)P=\log(1.995...\cdot6.4^{3{,}3219}.3219...*Q^3.3219...)P=\log(1.995...\cdot6.4^{3{,}321}.3219...*Q^3.3219...)P=\log(1.995...\cdot6.4^{3{,}32}.3219...*Q^3.3219...)P=\log(1.995...\cdot6.4^{3{,}3}.3219...*Q^3.3219...)P=\log(1.995...\cdot6.4^{3{,}}.3219...*Q^3.3219...)P=\log(1.995...\cdot6.4^3.3219...*Q^3.3219...)P=\log(1.995...6.4^3.3219...*Q^3.3219...)P=\log(1.995...*6.4^3.3219...*Q^3.3219...)P=(1.995...*6.4^3.3219...*Q^3.3219...)P=l(1.995...*6.4^3.3219...*Q^3.3219...)P=lo(1.995...*6.4^3.3219...*Q^3.3219...)

•Bereken 6,4^{3{,}3219\ldots}6,4^{3{,}3219\ldots}.6,4^{3{,}3219\ldots}.36,4^{3{,}3219\ldots}.326,4^{3{,}3219\ldots}.3216,4^{3{,}3219\ldots}.32196,4^{3{,}3219\ldots}.3219.6,4^{3{,}3219\ldots}.3219..6,4^{3{,}3219\ldots}.3219...6,4^{3{,}3219..}.3219...6,4^{3{,}3219.}.3219...6,4^{3{,}3219}.3219...6,4^{3{,}321}.3219...6,4^{3{,}32}.3219...6,4^{3{,}3}.3219...6,4^{3{,}}.3219...6,4^{3{,}4}.3219...6,4^{3{,}}.3219... (ongeveer476{,}509476509). P=\log(1{,}995...\cdot476{,}509...\cdot Q^{3{,}3219\ldots})P=\log(1{,}995...\cdot476509...\cdot Q^{3{,}3219\ldots})P=\log(1{,}995...\cdot476.509...\cdot Q^{3{,}3219\ldots})P=\log(1995...\cdot476.509...\cdot Q^{3{,}3219\ldots})P=\log(1.995...\cdot476.509...\cdot Q^{3{,}3219\ldots})P=\log(1.995...\cdot476.509...\cdot Q^{3{,}3219\ldots}.)P=\log(1.995...\cdot476.509...\cdot Q^{3{,}3219\ldots}.9)P=\log(1.995...\cdot476.509...\cdot Q^{3{,}3219\ldots}.9.)P=\log(1.995...\cdot476.509...\cdot Q^{3{,}3219\ldots}.9..)P=\log(1.995...\cdot476.509...\cdot Q^{3{,}3219\ldots}.9...)P=\log(1.995...\cdot476.509...\cdot Q^{3{,}3219\ldots}.39...)P=\log(1.995...\cdot476.509...\cdot Q^{3{,}3219\ldots}.329...)P=\log(1.995...\cdot476.509...\cdot Q^{3{,}3219\ldots}.3219...)P=\log(1.995...\cdot476.509...\cdot Q^{3{,}3219..}.3219...)P=\log(1.995...\cdot476.509...\cdot Q^{3{,}3219.}.3219...)P=\log(1.995...\cdot476.509...\cdot Q^{3{,}3219}.3219...)P=\log(1.995...\cdot476.509...\cdot Q^{3{,}321}.3219...)P=\log(1.995...\cdot476.509...\cdot Q^{3{,}32}.3219...)P=\log(1.995...\cdot476.509...\cdot Q^{3{,}3}.3219...)P=\log(1.995...\cdot476.509...\cdot Q^{3{,}}.3219...)P=\log(1.995...\cdot476.509...\cdot Q^3.3219...)P=\log(1.995...\cdot476.509...Q^3.3219...)P=\log(1.995...\cdot476.509...*Q^3.3219...)P=\log(1.995...476.509...*Q^3.3219...)P=\log(1.995...*476.509...*Q^3.3219...)P=(1.995...*476.509...*Q^3.3219...)P=l(1.995...*476.509...*Q^3.3219...)P=lo(1.995...*476.509...*Q^3.3219...)

•Vermenigvuldig de constanten en rond af op twee decimalen. P=\log(950{,}76\cdot Q^{3{,}32})P=\log(950{,}76\cdot Q^{3{,}32}.)P=\log(950{,}76\cdot Q^{3{,}32}.3)P=\log(950{,}76\cdot Q^{3{,}32}.32)P=\log(950{,}76\cdot Q^{3{,}3}.32)P=\log(950{,}76\cdot Q^{3{,}}.32)P=\log(950{,}76\cdot Q^3.32)P=\log(950{,}76Q^3.32)P=\log(950{,}76*Q^3.32)P=\log(95076*Q^3.32)P=\log(950.76*Q^3.32)P=(950.76*Q^3.32)P=l(950.76*Q^3.32)P=lo(950.76*Q^3.32) De formule is nu herleid naar de gewenste vorm P=\log(aQ^{B}), waarbija=950{,}76a=95076a=950.76=950.76 en b=3{,}32.b=332.b=3.32.=3.32.

Hoe herleid je naar een specifieke vorm door te ontbinden?

Soms moet je het argument van een logaritme ontbinden om een specifieke vorm te bereiken.

Rekenvoorbeeld: Schrijf de formule Y=^3\log(72x)Y=^3\log(72xz)Y=^3\log(72xz)Y=^3\log(72)Y=^3\log(72X)Y=^3(72X)Y=^{}(72X)Y=^3(72X)Y=^3\log_{\placeholder{}}(72X)Y=^3lo(72X)Y=^3l(72X)Y=^3(72X)Y=^3g(72X)Y=^{}g(72X)Y=^{\#}g(72X)Y=^{}g(72X)Y=^2g(72X)Y=^2lg(72X)Y=^2log(72X)Y=log(72X) in de vorm Y=2+3\log\left(ax\right)Y=2+3\log\left(ax\right)AY=2+3\log\left(ax\right)AXY=2+3\log\left(axAX\right)Y=2+3\log\left(aAX\right)Y=2+3\log\left(AX\right)Y=2+3\log AXY=2+3AXY=2+3lAXY=2+3loAX.

•Ontbind 72 zodanig dat er een macht van 3 ontstaat die je uit de logaritme kunt halen. 72=9\cdot872=98, en . Y=^3\log(9\cdot8\cdot x)Y=^3\log(9\cdot8\cdot)Y=^3\log(9\cdot8\cdot X)Y=^3\log(9\cdot8X)Y=^3\log(9\cdot8*X)Y=^3\log(98*X)Y=^3\log(9*8*X)Y=^3(9*8*X)Y=^3l(9*8*X)Y=^3lo(9*8*X)Y=^3log(9*8*X)Y=log(9*8*X)

•Splits de logaritme met regel 1. Y=^3\log\left(9\right)+^3\log\left(8x\right)Y=^3\log\left(9\right)+^3\log\left(8x\right)Y=^3\log\left(9\right)+^3\log\left(8\right)Y=^3\log\left(9\right)+^3\log\left(\right)Y=^3\log\left(9\right)+^3\logY=^3\log\left(9\right)+^3\log9Y=^3\log9)+^3\log9Y=^3\log\left(9)+^3\log9\right.Y=^3\log\left(9)+^3\log9)\right.Y=^3\log\left(9)+^3\log9)\right)Y=^3\log\left(9)+3log(8X\right)Y=^3\log\left(9+3log(8X\right)Y=^3\log\left(+3log(8X\right)Y9=^3\log\left(+3log(8X\right)Y=^3\log\left(+3log(8X\right)Y8=^3\log\left(+3log(8X\right)Y=^3\log\left(+3log(8X\right)Y=^3\log+3log(8X)Y=^3+3log(8X)Y=^3\log_{}+3log(8X)Y=^3\log_{\left(\placeholder{}\right)}+3log(8X)Y=^3\log_{\placeholder{}}+3log(8X)Y=^3lo+3log(8X)Y=^3l+3log(8X)Y=^3+3log(8X)Y=+3log(8X)Y=3+3log(8X)Y=3l+3log(8X)Y=3lo+3log(8X)Y=3log+3log(8X)

•Bereken ^3\log\left(9\right)^3\log\left(9\right)^3\log9. Omdat , is ^3\log\left(9\right)^3\log\left(9\right)^3\log9 gelijk aan 2. Y=2+^3\log(8x)Y=2+^3\log(8)Y=2+^3\log(8X)Y=2+^3(8X)Y=2+^3\log_{\placeholder{}}(8X)Y=2+^3lo(8X)Y=2+^3l(8X)Y=2+^3(8X)Y=2+^3\log_{\placeholder{}}(8X)Y=2+^3lo(8X)Y=2+^3l(8X)Y=2+^3(8X)Y=2+^3o(8X)Y=2+^3(8X)Y=2+^{}(8X)Y=2+^2(8X)Y=2+^{23}(8X)Y=2+^2(8X)Y=2+(8X)Y=2+3(8X)Y=2+3l(8X)Y=2+3lo(8X) De formule is nu herleid naar de gewenste vorm Y=2+3\log\left(ax\right), waarbij a=8=8.

Rekenvoorbeeld: Schrijf de formuleA=5\cdot^4\log(32B)A=5\cdot^4\log(32)A=5\cdot^4\log(32b)A=5^4\log(32b)A=^4\log(32b)A^4\log(32b)^4\log(32b)^4\log(32)^4\log(32B)^4(32B)(32B)\$(32B)(32B)4(32B)4l(32B)4lo(32B) in de vorm A=p+q\cdot^4\log\left(\frac12B\right)A=p+q\cdot^4\log\left(\frac12B\right)A=p+q\cdot^4\log\left(\frac12\right)A=p+q\cdot^4\log\left(\frac{1}{\placeholder{}}\right)A=p+q\cdot^4\log\left(1\right)A=p+q\cdot^4\log\left(\right)A=p+q\cdot^4\log\left(3\right)A=p+q\cdot^4\log\left(32\right)A=p+q\cdot^4\log\left(3\right)A=p+q\cdot^4\log\left(\right)A=p+q\cdot^4\logA=p+q\cdot^4A=p+q\cdotA=p+qA=p+A=pA=A=PA=P+.

A=5\cdot^4\log(32B)

•De gewenste vorm heeft '\frac12B\frac{1}{\placeholder{}}B1BB0B0.B' in de log. Herschrijf als een product: A=5\cdot^4\log(64\cdot\frac12B)A=5\cdot^4\log(64\cdot\frac{1}{\placeholder{}}B)A=5\cdot^4\log(64\cdot1B)A=5\cdot^4\log(64\cdot B)A=5\cdot^4\log(64\cdot0B)A=5\cdot^4\log(64\cdot0.B)A=5\cdot^4\log(64\cdot0.5B)A=5\cdot^4\log(640.5B)A=5\cdot^4\log(64*0.5B)A=5\cdot^4(64*0.5B)A=5\cdot^4l(64*0.5B)A=5\cdot^4lo(64*0.5B)A=5\cdot^4log(64*0.5B)A=5\cdot log(64*0.5B)A=5\cdot4log(64*0.5B)A=54log(64*0.5B)

•Splits de logaritme met regel 1. A=5\cdot(^4\log64+^4\log(\frac12B))A=5\cdot(^4\log64+^4\log(\frac{1}{}B))A=5\cdot(^4\log64+^4\log(\frac12B))A=5\cdot(^4\log64+^4\log(\frac{1}{\placeholder{}}B))A=5\cdot(^4\log64+^4\log(1B))A=5\cdot(^4\log64+^4\log(B))A=5\cdot(^4\log64+^4\log(0B))A=5\cdot(^4\log64+^4\log(0.B))A=5\cdot(^4\log64+^4\log(0.5B))A=5\cdot(^4\log64+^4(0.5B))A=5\cdot(^4\log64+^4l(0.5B))A=5\cdot(^4\log64+^4lo(0.5B))A=5\cdot(^4\log64+^4log(0.5B))A=5\cdot(^4\log64+log(0.5B))A=5\cdot(^4\log64+4log(0.5B))A=5\cdot(^464+4log(0.5B))A=5\cdot(^4l64+4log(0.5B))A=5\cdot(^4lo64+4log(0.5B))A=5\cdot(^4log64+4log(0.5B))A=5\cdot(log64+4log(0.5B))A=5\cdot(4log64+4log(0.5B))A=5(4log64+4log(0.5B))

•Bereken ^4\log\left(64\right)^4\log\left(64\right)^4\log64^464644644l644lo64. Omdat 64=4^364=464=4^ →^4\log\left(64\right)=3^4\log\left(64\right)=^4\log\left(64\right)^4\log\left(64\right.^4\log\left(64\right)^4\log\left(64\right)\left(\right)^4\log\left(64\right)^4\log64^464644644l644lo64. A=5\cdot(3+^4\log(\frac12B))A=5\cdot(3+^4\log(\frac{1}{\placeholder{}}B))A=5\cdot(3+^4\log(1B))A=5\cdot(3+^4\log(B))A=5\cdot(3+^4\log(0B))A=5\cdot(3+^4\log(0.B))A=5\cdot(3+^4\log(0.5B))A=5\cdot(3+^4(0.5B))A=5\cdot(3+(0.5B))A=5\cdot(3+4(0.5B))A=5\cdot(3+4l(0.5B))A=5\cdot(3+4lo(0.5B))A=5\cdot(3+4log(0.5B))A=5(3+4log(0.5B))

•Vermenigvuldig de termen in de haakjes met 5. A=15+5\cdot^4\log(1B)A=15+5\cdot^4\log(B)A=15+5\cdot^4\log(0B)A=15+5\cdot^4\log(0.B)A=15+5\cdot^4\log(0.5B)A=15+5\cdot^4(0.5B)A=15+5\cdot(0.5B)A=15+5\cdot4(0.5B)A=15+5\cdot4l(0.5B)A=15+5\cdot4lo(0.5B)A=15+5\cdot4log(0.5B)A=15+54log(0.5B) De formule is nu herleid naar de gewenste vorm A=p+q\cdot^4\log\left(\frac12B\right), waarbij p=15=15 en q=5=5.

Hoe bereken of herleid je tot één logaritme?

Door de rekenregels toe te passen, kunnen meerdere logaritmen vaak worden samengevoegd tot één logaritme of zelfs worden uitgerekend tot een enkel getal.

Rekenvoorbeeld: Bereken of herleid tot één logaritme: ^4\log\left(8\right)+^4\log\left(128\right)^4\log\left(8\right)+^4\log\left(128\right)^4\log\left(8\right)+^4\log128^4\log\left(8\right)+^4128^4\log\left(8\right)+^4l128^4\log\left(8\right)+^4lo128^4\log\left(8\right)+^4log128^4\log\left(8\right)+log128^4\log\left(8\right)+4log128^4\log\left(8+4log128\right)^4\log8+4log128^48+4log128^4l8+4log128^4lo8+4log128^4log8+4log128log8+4log128.

•Pas regel 1 toe: de som van twee logaritmen wordt de logaritme van het product. ^4\log(8\cdot128)^4\log(8128)^4\log(8*128)^4(8*128)(8*128)4(8*128)4l(8*128)4lo(8*128) ^4\log\left(1024\right)^4\log1024)^4\log1024^410241024410244l10244lo1024

•Herken dat 1024 een macht is van 4 (). ^4\log(4^5)^4(4^5)(4^5)4(4^5)4l(4^5)4lo(4^5)

•Pas regel 6 toe: de logaritme van een macht met hetzelfde grondtal als de logaritme, is de exponent. Dus: ^4\log(4^5)=5^4\log(4^5)=^4\log(4^5)

Rekenvoorbeeld: Herleid tot één logaritme: 1{,}5+^9\log\left(243\right)15+^9\log\left(243\right)1.5+^9\log\left(243\right)1.5+^9\log\left(243\right)l1.5+^9\log\left(243\right)lo1.5+^9\log\left(243\right)log1.5+^9\log\left(243\right)log21.5+^9\log\left(243\right)log241.5+^9\log\left(243\right)log2431.5+^9\log\left(243log243\right)1.5+^9\log\left(24log243\right)1.5+^9\log\left(2log243\right)1.5+^9\log\left(log243\right)1.5+^9\log log2431.5+^9log2431.5+log243.

•Zet de constante 1{,}515 om in een ^9\log^999l9lomet regel 6. ^9\log\left(9^{1{,}5}\right)+^9\log\left(243\right)^9\log\left(9^{1{,}5}\right)+^9\log\left(243\right)9^9\log\left(9^{1{,}5}\right)+^9\log\left(243\right)9l^9\log\left(9^{1{,}5}\right)+^9\log\left(243\right)9l^9\log\left(9^{1{,}5}\right)+^9\log\left(243\right)9lo^9\log\left(9^{1{,}5}\right)+^9\log\left(243\right)9lo4^9\log\left(9^{1{,}5}\right)+^9\log\left(243\right)9lo43^9\log\left(9^{1{,}5}\right)+^9\log\left(243\right)9log43^9\log\left(9^{1{,}5}\right)+^9\log\left(243\right)9log243^9\log\left(9^{1{,}5}\right)+^9\log\left(2439log243\right)^9\log\left(9^{1{,}5}\right)+^9\log\left(249log243\right)^9\log\left(9^{1{,}5}\right)+^9\log\left(29log243\right)^9\log\left(9^{1{,}5}\right)+^9\log\left(9log243\right)^9\log\left(9^{1{,}5}\right)+^9\log9log243^9\log\left(9^{1{,}5}\right)+^99log243^9\log\left(9^{1{,}5}\right)+9log243^9\log(9^{1{,}5}+9log243^9\log(9^{1{,}}+9log243\left.^9\log(9^{1{,}}\right)+9log243\left.^9\log(9^{1{,}5}\right)+9log243\left.^9\log(9^{1{,}5}5\right)+9log243\left.^9\log(9^{1{,}}5\right)+9log243\left.^9\log(9^15\right)+9log243\left.^9\log(9^1.5\right)+9log243\left.^9(9^1.5\right)+9log243\left.(9^1.5\right)+9log243\left((9^1.5\right)+9log243\left(9(9^1.5\right)+9log243\left((9^1.5\right)+9log243(9^1.5)+9log2439(9^1.5)+9log2439l(9^1.5)+9log2439lo(9^1.5)+9log243

•Bereken 9^{1{,}5}=9^{\left(\frac32\right)}=(\surd9)^3=3^3=279^{1{,}5}=9^{\left(\frac32\right)}=(\surd9)^3=3^3=29^{1{,}5}=9^{\left(\frac32\right)}=(\surd9)^3=3^3=9^{1{,}5}=9^{\left(\frac32\right)}=(\surd9)^3=3^39^{1{,}5}=9^{\left(\frac32\right)}=(\surd9)^3=39^{1{,}5}=9^{\left(\frac32\right)}=(\surd9)^3=9^{1{,}5}=9^{\left(\frac32\right)}=(\surd9)^39^{1{,}5}=9^{\left(\frac32\right)}=9^{1{,}5}=9^{\left(\frac32\right)}9^{1{,}5}=9^{(\frac32}9^{1{,}5}=9^{(\frac32}39^{1{,}5}=9^{(\frac32}3/9^{1{,}5}=9^{(\frac32}3/29^{1{,}5}=9^{(\frac{3}{\placeholder{}}}3/29^{1{,}5}=9^{(3}3/29^{1{,}5}=9^{(}3/29^{1{,}}=9^{(}3/29^1=9^{(}3/29^1.=9^{(}3/2 ^9\log\left(27\right)+^9\log\left(243\right)^9\log\left(27\right)+^9\log\left(243\right)^9\log\left(27\right)+^9\log243^9\log\left(27\right)+^9243^9\log\left(27\right)+^9l243^9\log\left(27\right)+^9lo243^9\log\left(27\right)+^9log243^9\log\left(27\right)+log243^9\log\left(27\right)+9log243^9\log\left(27+9log243\right)^9\log\left(2+9log243\right)^9\log\left(+9log243\right)^9\log+9log243^9\log2+9log243^9\log27+9log243^927+9log24327+9log243927+9log2439l27+9log2439lo27+9log243

•Pas regel 1 toe: de som van twee logaritmen wordt de logaritme van het product. \left.^9\log(27\cdot243)\right.\left.^9\log(27\cdot243\right)\left.^9\log(27243\right)\left.^9\log(27*243\right)\left.^9(27*243\right)\left.(27*243\right)\left.(27*243\right)\left((27*243\right)(27*243)9(27*243)9l(27*243)9lo(27*243) ^9\log\left(6561\right)^9\log\left(6561\right)^9\log6561^965616561965619l65619lo6561

•Herken dat 6561 een macht is van 9 (6561=9^46561=96561=9^). ^9\log(9^4)^9(9^4)(9^4)9(9^4)9l(9^4)9lo(9^4)

•Pas regel 6 toe. ^9\log(9^4)

Rekenvoorbeeld: Herleid tot één logaritme: \frac12\cdot\log\left(25\right)+^{\frac12}\log\left(16\right)\frac12\cdot\log\left(25\right)+^{\frac12}\log\left(16\right)\frac12\cdot\log\left(25\right)+^{\frac12}\log\left(1\right)\frac12\cdot\log\left(25\right)+^{\frac12}\log\left(\right)\frac12\cdot\log\left(25\right)+^{\frac12}\log\frac12\cdot\log\left(25\right)+^{\frac12}\frac12\cdot\log\left(25\right)+^{\frac12}l16\frac12\cdot\log\left(25\right)+^{\frac12}l16\frac12\cdot\log\left(25\right)+^{\frac12}lo16\frac12\cdot\log\left(25\right)+^{\frac12}log16\frac12\cdot\log\left(25\right)+^{\frac{1}{\placeholder{}}}log16\frac12\cdot\log\left(25\right)+^1log16\frac12\cdot\log\left(25\right)+\frac{^1}{\placeholder{}}log16\frac12\cdot\log\left(25\right)+^1log16\frac12\cdot\log\left(25\right)+\frac{^1}{\placeholder{}}log16\frac12\cdot\log\left(25\right)+^1log16\frac12\cdot\log\left(25\right)+log16\frac12\cdot\log\left(25\right)+0log16\frac12\cdot\log\left(25\right)+0.log16\frac12\cdot\log\left(25\right)+0.5log16\frac12\cdot\log\left(25+0.5log16\right)\frac12\cdot\log25+0.5log16\frac12\cdot25+0.5log16\frac12\cdot log25+0.5log16\frac12log25+0.5log16\frac{1}{\placeholder{}}log25+0.5log161log25+0.5log16log25+0.5log160log25+0.5log160.log25+0.5log16.

•\frac12\frac{1}{\placeholder{}}11.1.21.1verplaatst naar \log\left(25\right)\log\left(25\right)\log\left(2\right)\log\left(\right)\log

\log\left(25^{\frac12}\right)=\log\left(\sqrt{25}\right)=\log\left(5\right)\log\left(25^{\frac12}\right)=\log\left(\sqrt{25}\right)=\log\left(5\right)\log\left(25^{\frac12}\right)=\log\left(\sqrt{25}\right)=\log\left(\right)\log\left(25^{\frac12}\right)=\log\left(\sqrt{25}\right)=\log\log\left(25^{\frac12}\right)=\log\left(\sqrt{25}\right)=\log\left(25^{\frac12}\right)=\log\left(\sqrt{25}\right)\log\left(25^{\frac12}\right)=\log\left(\sqrt{25}\right)\log\left(25^{\frac12}\right)=\log\left(\sqrt2\right)\log\left(25^{\frac12}\right)=\log\left(\sqrt{\placeholder{}}\right)\log\left(25^{\frac12}\right)=\log\left(\right)\log\left(25^{\frac12}\right)=\log\log\left(25^{\frac12}\right)=\log\left(25^{\frac12}\right)\log\left(25^{\frac12}\right)\log\left(25^{\frac{1}{\placeholder{}}}\right)\log\left(25^1\right)\log\left(25\right)\log\left(2\right)\log\left(\right)\log

•Pas regel 6 toe voor het tweede deel.

^{\frac12}\log\left(2^4\right)^{\frac12}\log\left(\right.2^4^{\frac12}\log\left(\right.2^{\frac12}\log\left(\right.^{\frac12}\log\left(1\right.^{\frac12}\log\left(16\right.^{\frac12}\log\left(16\right)^{\frac12}\log\left(16\right)=^{\frac12}\log\left(16\right)^{\frac12}\log\left(16\right)^{\frac12}\log\left(1\right)^{\frac12}\log\left(\right)^{\frac12}\log^{\frac12}^{\frac{1}{\placeholder{}}}^1

^{\frac12}\log\left(\left(2^{-1}\right)^{-4}\right)^{\frac12}\log\left(2^{-1}\right)^{-4})^{\frac12}\log\left(2^{-1}\right)^{-4}^{\frac12}\log\left(2^{-1}\right)^{-}^{\frac12}\log\left(2^{-1}\right)^{-)}^{\frac12}\log\left(2^{-1}\right)^{-4)}^{\frac12}\log\left(2^{-1}\right)^{-4}^{\frac12}\log\left(2^{-1}\right)^{-}^{\frac12}\log\left(2^{-1}\right)^{\frac12}\log\left(2^{-1}\right)^{\frac12}\log\left(2^{-10}\right)^{\frac12}\log\left(2^{-1}\right)^{\frac12}\log\left(2^{-}\right)^{\frac12}\log\left(2\right)^{\frac12}\log\left(\right)^{\frac12}\log^{\frac12}^{\frac{1}{\placeholder{}}}^1

^{\frac12}\log\left(\left(\frac12^{}\right)^{-4}\right)^{\frac12}\log\left(\left(\frac12^{}\right)^{-}\right)^{\frac12}\log\left(\left(\frac12^{}\right)^{-5}\right)^{\frac12}\log\left(\left(\frac12^{}\right)^{-54}\right)^{\frac12}\log\left(\left(\frac12^{}\right)^{-54}\right)^{\frac12}\log\left(\left(\frac12^{}\right)^{-}\right)^{\frac12}\log\left(\left(\frac12^{}\right)^{}\right)^{\frac12}\log\left(\left(\frac12^{}\right)^0\right)^{\frac12}\log\left(\left(\frac12^{}\right)^04\right)^{\frac12}\log\left(\left(\frac12^{}\right)^0\right)^{\frac12}\log\left(\left(\frac12^{}\right)\right)^{\frac12}\log\left(\left(\frac12^{}\right.\right)^{\frac12}\log\left(\left(\frac12^{-}\right.\right)^{\frac12}\log\left(\left(\frac12^{-4}\right.\right)^{\frac12}\log\left(\left(\frac12^{-4}\right)\right)^{\frac12}\log\left(\left(\frac12\right)\right)^{-4}^{\frac12}\log\left(\left(\frac12\right)\right)_{}^{-4}^{\frac12}\log\left(\left(\frac12\right)\right)_{)}^{-4}^{\frac12}\log\left(\left(\frac12\right)\right)^{-4}^{\frac12}\log\left(\left(\frac12\right)\right)^{-4)}^{\frac12}\log\left(\left(\frac12\right)\right)^{-4}^{\frac12}\log\left(\left(\frac12\right)\right)^{-}^{\frac12}\log\left(\left(\frac12\right)\right)^{\frac12}\log\left(\left(\frac12\right)\right)^{\frac12}\log\left(\left(\frac12\right)\right)^{\frac12}\log\left(\left(1\right)\right)^{\frac12}\log\left(\left(\right)\right)^{\frac12}\log\left(\right)^{\frac12}\log^{\frac12}^{\frac{1}{\placeholder{}}}^1

\log\left(5\right)-4\log\left(5\right)-\log\left(5\right)\log\left(5\right)\log\left(\right)\log\log5\logl

•4 omschrijven naar logaritme met grondtal 10.

\log\left(5\right)-\log\left(10^4\right)\log\left(5\right)-\log\left(10^4\right.\log\left(5\right)-\log\left(10\right.\log\left(5\right)-\log\left(1\right.\log\left(5\right)-\log\left(1\right)\log\left(5\right)-\log\left(1\right)^{}\log\left(5\right)-\log\left(1\right)^4\log\left(5\right)-\log\left(1\right)\log\left(5\right)-\log\left(1\right)\log\left(5\right)-\log\left(1\right)\log\left(5\right)-\log\log\left(5\right)-\log\left(5\right)\log\left(5\right)=\log\left(5\right)\log\left(5\right)\log\left(\right)\log

\log\left(5\right)-\log\left(10000\right)\log\left(5\right)-\log\left(1000\right)\log\left(5\right)-\log\left(1000\right.\log\left(5\right)-\log\left(100\right.\log\left(5\right)-\log\left(100\right.\log\left(5\right)-\log\left(1\right.\log\left(5\right)-\log\left(\right.\log\left(5\right)-\log\left(2\right.\log\left(5\right)-\log\left(2\right.\log\left(5\right)-\log\left(2\right)1\log\left(5\right)-\log\left(2\right)10\log\left(5\right)-\log\left(2\right)100\log\left(5\right)-\log\left(2\right)100\log\left(5\right)-\log\left(2\right)1\log\left(5\right)-\log\left(2\right)\log\left(5\right)-\log\left(2\right)\log\left(5\right)-\log\left(20\right)\log\left(5\right)-\log\left(200\right)\log\left(5\right)-\log\left(20\right)\log\left(5\right)-\log\left(2\right)\log\left(5\right)-\log\left(\right)\log\left(5\right)-\log\log\left(5\right)-\log\left(5\right)\log\left(5\right)=\log\left(5\right)\log\left(5\right)\log\left(\right)\log\log9\log

•Pas regel 2 toe: Het verschil van twee logaritmen met hetzelfde grondtal is de logaritme van het quotiënt van de argumenten

\log\frac{5}{10000}=\log\left(0{,}0005\right)\log\frac{5}{10000}=\log\left(0{,}0005\right)\log\frac{5}{10000}=\log\left(0{,}000\right)\log\frac{5}{10000}=\log\left(0{,}00\right)\log\frac{5}{10000}=\log\left(0{,}0\right)\log\frac{5}{10000}=\log\left(0{,}\right)\log\frac{5}{10000}=\log\left(0\right)\log\frac{5}{10000}=\log\left(\right)\log\frac{5}{10000}=\log\log\frac{5}{10000}=\log\frac{5}{10000}\log\frac{5}{1000}\log\frac{5}{100}\log\frac{5}{100}\log\frac{5}{10}\log\frac{5}{\placeholder{}}\log5\log

•Het kan niet verder berekend worden