SOLVING EQUATIONS WITH EXCEL









Math 3201 - 7.4B Word Problems Involving Logarithms

Example 2: Kelly invests $5000 with a bank. The value of her investment can be determined using the formula = 5000(1.06) where is the value of the 
math ch . bnotes workings


Worksheet: Logarithmic Function

Solve the following logarithmic equations. (1) lnx = −3. (2) log(3x − 2) = 2. (3) 2 log x 
Exercises LogarithmicFunction


APPLICATIONS OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS

EARTHQUAKE WORD PROBLEMS: As with any word problem the trick is convert a narrative statement or question to a mathematical statement. Before we start
EarthquakeWordProblems


Logarithmic Equations Examples And Solutions Pdf

solutions are equations with solution and logarithmic equation and provide guidance on solutions. Solving Logarithmic Equations Word Problems Example 1.
logarithmic equations examples and solutions pdf





Solving Logarithmic Equations (Word Problems)

Solving Logarithmic Equations (Word Problems). Example 1 The equation of an exponential function that models the subscription data.
Solving Logarithmic Equations Word Problems


The Ontario Curriculum Grades 11 and 12: Mathematics

http://www.edu.gov.on.ca/eng/curriculum/secondary/math1112currb.pdf


LOGARITHMS

Evaluate the solution to logarithmic equations to find extraneous roots. this relationship to solve problems involving logarithms and exponents.
filedownload.ashx?moduleinstanceid= &dataid= &FileName= LOGARITHMS


SOLVING EQUATIONS WITH EXCEL

that the first step of all Excel solutions is to correctly define the function we want to equations containing exponential or logarithmic functions.
Solving equations with Excel





Exponential Growth and Decay Word Problems - Write an equation

doubling. If we start with only one bacteria which can double every hour how many bacteria will we have by the end of one day?
Growth Decay Word Problem Key


6.2 Properties of Logarithms

In Section 6.1 we introduced the logarithmic functions as inverses of The reader is encouraged to look through the solutions to Example 6.2.1 to see ...
S&Z . & .


215056 SOLVING EQUATIONS WITH EXCEL

Page1of6

SOLVINGEQUATIONSWITHEXCEL

ExcelandLotussoftwareareequippedwithfunctionsthatallowtheusertoidentifythe rootofanequation.Byroot,wemeanthevaluesofxsuchthatagivenequationcancels itselfout. Letusconsiderthecasewherewewishtoobtaintherootofthefunction i.e.,solvetheequationʹݔ thatthe firststepofallExcelsolutionsistocorrectlydefinethefunctionwewanttofind therootof,andtoassignthevariabletoonespecificcell. WeassignedthecellB1tocontainthevalueofvariablex.IncellB2,wedefinethe function.NotethatB1playsthepartofݔintheformula.ByinsertingvaluesincellB1, youwillnoticethattheresultofthefunctionwillchange.Therefore,findingtherootof afunctionimpliesfindingthevalueofݔsuchthatthefunctioniszero.Ourgoalisto havecellB1vary(thevalueofx)untilthecellB2(thatcontainsthevalueofthe function)is0. Itwouldbetoolongtofindananswerbytrialanderror.SelectinExcelthefunction Solver(Toolsmenu).Thefollowingdialogboxwillappear.

Page2of6

SetTargetCell:weaskyoutoidentifythepositionofthefunctionyouwishtocarryout anoperationon.Inourexample,thefunctionwasplacedincellB2. Equalto:ToidentifytheoperationyouwishtocarryoutwiththefunctionlocatedatB2 (max? min?value?).Wewantthefunctiontotakeonthevalue0. ByChangingCells:Toidentifycellsthatcontainthevariablesofthefunction.Inour example,B1isthecellcontainingthevalueofx.

ByclickingonSolve,Excelwillexecutetheoperationyou

askedittoandwillgiveyou thesolutionx=0,85078105. OneofthelimitsoftheExcelSolveristhatitwillonlygiveonerooteventhoughwe knowthereisasecondone.Fornow,weusethediscriminant t= Thatgivesthesecondroot(ݔ ൌെʹǡ͵ͷͲ͹ͺͳͲͺ).

Page3of6

Unfortunately,thediscriminantwillbeofnousewithothertypesoffunctionsandwe willnotbeabletocountonittohelpus.

ExponentialandlogarithmicequationsusingExcel

Besidesforfindingtherootofpolynomialequations,theExcelSolvercansolve equationscontainingexponentialorlogarithmic functions.Thesoftwarewillbeallthe moreusefulinthiscasesincesolvingthistypeofalgebraicequationsisoftenimpossible. Forexample,therearenosolutionmethodsthatwillfindthevalueofݔsuchthatthe equation݁ presentedinthecaseofroots,exceptforthefollowingdetail:theequationmustbe rewrittensothatalltermsareregroupedontheleftsideoftheequality.Forexample, insteadofresolvingtheequation

Example

Solvethefollowingequationwiththehelpofthesolver:݁

Solution

Firstly,weneedtorewritetheequalitysothatthetermsareregroupedontheleftside: aswellasattributingthevariabletoaspecificcell.

Page4of6

Onceagain,wehavedesignatedthecellB1tocontainthevalueofthevariableݔ.The cellB2containstheexpressionequalto0.ItisdefinedinfunctiontoB1,which substitutesthevariableݔ. SelectinExcelthefunctionSolver(Toolsmenu).Adialogboxwill appearinwhichyou needtofillininformation. Equalto:Toidentifytheoperationyouwishtocarryoutwith(max?min?value?). Variablecells:Toidentifycellsthatcontainthevariablesofthefunction.Inour example,B1isthecellcontainingthevalue ofx.

Targetcelltodefine:thefunctionwasplacedincellB2.

Equalto:WewantthefunctionlocatedinB2totakeonthevalue0. Variablecells:B1isthecellthatwillcontainthevalueofݔ. ByclickingonSolve,Excelwillexecutetheoperationyouaskedittoandwillgiveyou thefollowinganswer:

Page5of6

thatExcelonlygivesonesolutiontoanygivenequation,eventhoughitmayhavemore

thanone.Asecondsolutionexistswhenݔ ൌ ʹǡͳͷ͵ʹͻʹͳ͹,asisindicatedinthe

followingimage: Thetechniquesallowingustofindtheseothersolutionswillbethe subjectoffuture discussions.

Page6of6

Exercise

WiththehelpofExcel,findatleastonevalueofxsuchthatthefollowingequationsare satisfied. a) ݔ ൅ ݔ c) ݁ d) ݔ െ ݁

Solution

a. 1,68957994 b. 0,76822112 c. 0,44754188 d. 0,82461277

Page1of6

SOLVINGEQUATIONSWITHEXCEL

ExcelandLotussoftwareareequippedwithfunctionsthatallowtheusertoidentifythe rootofanequation.Byroot,wemeanthevaluesofxsuchthatagivenequationcancels itselfout. Letusconsiderthecasewherewewishtoobtaintherootofthefunction i.e.,solvetheequationʹݔ thatthe firststepofallExcelsolutionsistocorrectlydefinethefunctionwewanttofind therootof,andtoassignthevariabletoonespecificcell. WeassignedthecellB1tocontainthevalueofvariablex.IncellB2,wedefinethe function.NotethatB1playsthepartofݔintheformula.ByinsertingvaluesincellB1, youwillnoticethattheresultofthefunctionwillchange.Therefore,findingtherootof afunctionimpliesfindingthevalueofݔsuchthatthefunctioniszero.Ourgoalisto havecellB1vary(thevalueofx)untilthecellB2(thatcontainsthevalueofthe function)is0. Itwouldbetoolongtofindananswerbytrialanderror.SelectinExcelthefunction Solver(Toolsmenu).Thefollowingdialogboxwillappear.

Page2of6

SetTargetCell:weaskyoutoidentifythepositionofthefunctionyouwishtocarryout anoperationon.Inourexample,thefunctionwasplacedincellB2. Equalto:ToidentifytheoperationyouwishtocarryoutwiththefunctionlocatedatB2 (max? min?value?).Wewantthefunctiontotakeonthevalue0. ByChangingCells:Toidentifycellsthatcontainthevariablesofthefunction.Inour example,B1isthecellcontainingthevalueofx.

ByclickingonSolve,Excelwillexecutetheoperationyou

askedittoandwillgiveyou thesolutionx=0,85078105. OneofthelimitsoftheExcelSolveristhatitwillonlygiveonerooteventhoughwe knowthereisasecondone.Fornow,weusethediscriminant t= Thatgivesthesecondroot(ݔ ൌെʹǡ͵ͷͲ͹ͺͳͲͺ).

Page3of6

Unfortunately,thediscriminantwillbeofnousewithothertypesoffunctionsandwe willnotbeabletocountonittohelpus.

ExponentialandlogarithmicequationsusingExcel

Besidesforfindingtherootofpolynomialequations,theExcelSolvercansolve equationscontainingexponentialorlogarithmic functions.Thesoftwarewillbeallthe moreusefulinthiscasesincesolvingthistypeofalgebraicequationsisoftenimpossible. Forexample,therearenosolutionmethodsthatwillfindthevalueofݔsuchthatthe equation݁ presentedinthecaseofroots,exceptforthefollowingdetail:theequationmustbe rewrittensothatalltermsareregroupedontheleftsideoftheequality.Forexample, insteadofresolvingtheequation

Example

Solvethefollowingequationwiththehelpofthesolver:݁

Solution

Firstly,weneedtorewritetheequalitysothatthetermsareregroupedontheleftside: aswellasattributingthevariabletoaspecificcell.

Page4of6

Onceagain,wehavedesignatedthecellB1tocontainthevalueofthevariableݔ.The cellB2containstheexpressionequalto0.ItisdefinedinfunctiontoB1,which substitutesthevariableݔ. SelectinExcelthefunctionSolver(Toolsmenu).Adialogboxwill appearinwhichyou needtofillininformation. Equalto:Toidentifytheoperationyouwishtocarryoutwith(max?min?value?). Variablecells:Toidentifycellsthatcontainthevariablesofthefunction.Inour example,B1isthecellcontainingthevalue ofx.

Targetcelltodefine:thefunctionwasplacedincellB2.

Equalto:WewantthefunctionlocatedinB2totakeonthevalue0. Variablecells:B1isthecellthatwillcontainthevalueofݔ. ByclickingonSolve,Excelwillexecutetheoperationyouaskedittoandwillgiveyou thefollowinganswer:

Page5of6

thatExcelonlygivesonesolutiontoanygivenequation,eventhoughitmayhavemore

thanone.Asecondsolutionexistswhenݔ ൌ ʹǡͳͷ͵ʹͻʹͳ͹,asisindicatedinthe

followingimage: Thetechniquesallowingustofindtheseothersolutionswillbethe subjectoffuture discussions.

Page6of6

Exercise

WiththehelpofExcel,findatleastonevalueofxsuchthatthefollowingequationsare satisfied. a) ݔ ൅ ݔ c) ݁ d) ݔ െ ݁

Solution

a. 1,68957994 b. 0,76822112 c. 0,44754188 d. 0,82461277
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