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
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Solving Logarithmic Equations (Word Problems)
Solving Logarithmic Equations (Word Problems). Example 1. INVESTMENT Mr. and Mrs. Mitchell are saving for their daughter's college education. They.
Solving Logarithmic Equations Word Problems
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
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
LOGARITHMS
Evaluate the solution to logarithmic equations to find extraneous roots. this relationship to solve problems involving logarithms and exponents.
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Worksheet: Logarithmic Function
Solve the following logarithmic equations. (1) lnx = −3. (2) log(3x − 2) = 2. (3) 2 log x
Exercises LogarithmicFunction
Exponential and Logarithmic Equations and Applications
3. If necessary solve for r
. Exponential and Logarithmic Equations and Applications
Exponential growth occurs when a quantity increases by the same
Day 7: Solving Exponential Word Problems involving Logarithms. Warm – Up Example 1: “Growth” ... Graphs of Logarithmic Functions.
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Bookmark File PDF Exponential Growth And Decay Word Problems
Find the value of the investment after 5 years.' An example of an exponential decay word problem is the following: 'The value of a new $35000 car Logarithm ...
Section 4.3 Logarithmic Functions
The logarithm properties often arise when solving problems involving logarithms. First we'll look at a simpler log equation. Example 5. Solve .
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Vanier College Sec V Mathematics
Department of Mathematics 201-015-50Worksheet: Logarithmic Function1. Find the value ofy.
(1) log525 =y(2) log31 =y(3) log164 =y(4) log218
=y (5) log51 =y(6) log28 =y(7) log717
=y(8) log319 =y (9) log y32 = 5 (10) log9y=12 (11) log418 =y(12) log9181 =y2. Evaluate.
(1) log31 (2) log44 (3) log773(4)blogb3(3) log2553(4) 16log48
3. Write the following expressions in terms of logs ofx,yandz.
(1) logx2y(2) logx3y2z (3) logpx 3py 2z4(4) logxyz
(5) log xyz (6) logxy 2 (7) log(xy)13 (8) logxpz (9) log 3px 3 pyz (10) log4rx 3y2z4(11) logxrpx
z (12) logrxy 2z 84. Write the following equalities in exponential form.
(1) log381 = 4 (2) log77 = 1 (3) log12
18 = 3 (4) log31 = 0 (5) log 4164=3 (6) log6136 =2 (7) logxy=z(8) logmn=12
5. Write the following equalities in logarithmic form.
(1) 82= 64 (2) 103= 10000 (3) 42=116
(4) 34=181 (5) 12 5 = 32 (6)13 3 = 27 (7)x2z=y(8)px=y6. True or False?
(1) log xy 3 = logx3logy(2) log(ab) = logalogb(3) logxk=klogx (4) (loga)(logb) = log(a+b) (5)logalogb= log(ab) (6) (lna)k=klna (7) log aaa=a(8)ln1x = lnx(9) lnpx xk= 2k7. Solve the following logarithmic equations.
(1) lnx=3 (2) log(3x2) = 2 (3) 2logx= log2 + log(3x4) (4) logx+ log(x1) = log(4x) (5) log3(x+ 25)log3(x1) = 3 (6) log9(x5) + log9(x+ 3) = 1
(7) logx+ log(x3) = 1 (8) log2(x2) + log2(x+ 1) = 28. Prove the following statements.
(1) log pb x= 2logbx(2) log1pb px=logbx(3) logb4x2= logbpx9. Given that log2 =x, log3 =yand log7 =z, express the following expressions
in terms ofx,y, andz. (1) log12 (2) log200 (3) log 143(4) log0:3 (5) log1:5 (6) log10:5 (7) log15 (8) log60007
10. Solve the following equations.
(1) 3 x2 = 12 (2) 31x= 2 (3) 4 x= 5x+1(4) 61x= 10x (5) 32x+1= 2x2(6)101 +ex= 2
(7) 52x5x12 = 0 (8)e2x2ex= 15
11. Draw the graph of each of the following logarithmic functions, and analyze each
of them completely. (1)f(x) = logx(2)f(x) = logx (3)f(x) =log(x3) (4)f(x) =2log3(3x) (5)f(x) =ln(x+ 1) (6)f(x) = 2ln12 (x+ 3) (7)f(x) = ln(2x+ 4) (8)f(x) =2ln(3x+ 6)12. Find the inverse of each of the following functions.
(1)f(x) = log2(x3)5 (2)f(x) = 3log3(x+ 3) + 1 (3)f(x) =2log2(x1) + 2 (4)f(x) =ln(12x) + 1 (5)f(x) = 2x3 (6)f(x) = 233x1 (7)f(x) =5ex+ 2 (8)f(x) = 12e2x13. 15 000$ is invested in an account that yeilds 5% interest per year. After how
many years will the account be worth 91 221.04$ if the interest is compounded yearly?14. 8 000$ is invested in an account that yeilds 6% interest per year. After how
many years will the account be worth 13709.60$ if the interest is compounded monthly?15. Starting at the age of 40, an average man loses 5% of his hair every year. At
what age should an average man expect to have half his hair left?16. A bacteria culture starts with 10 00 bacteria and the number doubles every 40
minutes. (a) Find a formula for the number of bacteria at time t. (b) Find the number of bacteria after one hour. (c) After how many minutes will there be 50 000 bacteria?ANSWERS
1. (1) 2
(2) 0 (3) 12 (4)3 (5) 0 (6) 3 (7)1 (8)2 (9) 2 (10) 13 (11)32 (12)22. (1) 0
(2) 1 (3) 3 (4) 3 (5) 32(6) 643. (1) 2logx+ logy (2) 3logx+ 2logylogz (3) 12 logx+23 logy4logz (4) logx+ logy+ logz (5) logxlogylogz (6) 2logx2logy (7)
Vanier College Sec V Mathematics
Department of Mathematics 201-015-50Worksheet: Logarithmic Function1. Find the value ofy.
(1) log525 =y(2) log31 =y(3) log164 =y(4) log218
=y (5) log51 =y(6) log28 =y(7) log717
=y(8) log319 =y (9) log y32 = 5 (10) log9y=12 (11) log418 =y(12) log9181 =y2. Evaluate.
(1) log31 (2) log44 (3) log773(4)blogb3(3) log2553(4) 16log48
3. Write the following expressions in terms of logs ofx,yandz.
(1) logx2y(2) logx3y2z (3) logpx 3py 2z4(4) logxyz
(5) log xyz (6) logxy 2 (7) log(xy)13 (8) logxpz (9) log 3px 3 pyz (10) log4rx 3y2z4(11) logxrpx
z (12) logrxy 2z 84. Write the following equalities in exponential form.
(1) log381 = 4 (2) log77 = 1 (3) log12
18 = 3 (4) log31 = 0 (5) log 4164=3 (6) log6136 =2 (7) logxy=z(8) logmn=12
5. Write the following equalities in logarithmic form.
(1) 82= 64 (2) 103= 10000 (3) 42=116
(4) 34=181 (5) 12 5 = 32 (6)13 3 = 27 (7)x2z=y(8)px=y6. True or False?
(1) log xy 3 = logx3logy(2) log(ab) = logalogb(3) logxk=klogx (4) (loga)(logb) = log(a+b) (5)logalogb= log(ab) (6) (lna)k=klna (7) log aaa=a(8)ln1x = lnx(9) lnpx xk= 2k7. Solve the following logarithmic equations.
(1) lnx=3 (2) log(3x2) = 2 (3) 2logx= log2 + log(3x4) (4) logx+ log(x1) = log(4x) (5) log3(x+ 25)log3(x1) = 3 (6) log9(x5) + log9(x+ 3) = 1
(7) logx+ log(x3) = 1 (8) log2(x2) + log2(x+ 1) = 28. Prove the following statements.
(1) log pb x= 2logbx(2) log1pb px=logbx(3) logb4x2= logbpx9. Given that log2 =x, log3 =yand log7 =z, express the following expressions
in terms ofx,y, andz. (1) log12 (2) log200 (3) log 143(4) log0:3 (5) log1:5 (6) log10:5 (7) log15 (8) log60007
10. Solve the following equations.
(1) 3 x2 = 12 (2) 31x= 2 (3) 4 x= 5x+1(4) 61x= 10x (5) 32x+1= 2x2(6)101 +ex= 2
(7) 52x5x12 = 0 (8)e2x2ex= 15
11. Draw the graph of each of the following logarithmic functions, and analyze each
of them completely. (1)f(x) = logx(2)f(x) = logx (3)f(x) =log(x3) (4)f(x) =2log3(3x) (5)f(x) =ln(x+ 1) (6)f(x) = 2ln12 (x+ 3) (7)f(x) = ln(2x+ 4) (8)f(x) =2ln(3x+ 6)12. Find the inverse of each of the following functions.
(1)f(x) = log2(x3)5 (2)f(x) = 3log3(x+ 3) + 1 (3)f(x) =2log2(x1) + 2 (4)f(x) =ln(12x) + 1 (5)f(x) = 2x3 (6)f(x) = 233x1 (7)f(x) =5ex+ 2 (8)f(x) = 12e2x13. 15 000$ is invested in an account that yeilds 5% interest per year. After how
many years will the account be worth 91 221.04$ if the interest is compounded yearly?14. 8 000$ is invested in an account that yeilds 6% interest per year. After how
many years will the account be worth 13709.60$ if the interest is compounded monthly?15. Starting at the age of 40, an average man loses 5% of his hair every year. At
what age should an average man expect to have half his hair left?16. A bacteria culture starts with 10 00 bacteria and the number doubles every 40
minutes. (a) Find a formula for the number of bacteria at time t. (b) Find the number of bacteria after one hour. (c) After how many minutes will there be 50 000 bacteria?ANSWERS
1. (1) 2
(2) 0 (3) 12 (4)3 (5) 0 (6) 3 (7)1 (8)2 (9) 2 (10) 13 (11)32 (12)22. (1) 0
(2) 1 (3) 3 (4) 3 (5) 32(6) 643. (1) 2logx+ logy (2) 3logx+ 2logylogz (3) 12 logx+23 logy4logz (4) logx+ logy+ logz (5) logxlogylogz (6) 2logx2logy (7)