Properties of Logarithms.pdf
Worksheet by Kuta Software LLC. Condense each expression to a single logarithm. 13) log 3 − log 8. 14) log 6. 3. 15) 4log 3 − 4log 8. 16) log 2 + log 11 + log
Worksheet: Logarithmic Function
Solve the following logarithmic equations. (1) lnx = −3. (2) log(3x − 2) = 2. (3) 2 log x
Worksheet - Laws of Logarithms (Power Product and Quotient)
Expand the following logarithms using one or more of the logarithm rules. 9. logs. 12a. 2. = 11. log √√x³y. X. = 5. 10. log₂. 12. icg.
Worksheet 2.7 Logarithms and Exponentials
Worksheet 2.7 Logarithms and Exponentials. Section 1 Logarithms. The mathematics of (a) Use log laws to solve log3 x = log3 7 + log3 3. (b) Without tables ...
Mathcentre
explain what is meant by a logarithm. • state and use the laws of logarithms. • solve simple equations requiring the use of logarithms. Contents. 1.
Properties of Logarithms Worksheet
The following examples show how to expand logarithmic expressions using each of the rules above. Example 1. Expand log2493 log2493 = 3 • log249. Use the Power
LOGARITHMS
11.0 Students prove simple laws of logarithms. 11.1 Students understand the inverse relationship between exponents and logarithms and use this relationship
LOGARITHMS EXAM QUESTIONS
Solve each of the following logarithmic equations. a) log 16 log 9 2 x x. = + . b)
Math 3 Unit 9: Logarithms Additional Clovis Unified Resources http
Worksheet 6. Math 3 Unit 9 Worksheet 6. Name: Solving Logarithmic Equations Using the Laws of Logarithms. Date: :_____.
Worksheet: Logarithmic Function
Solve the following logarithmic equations. (1) lnx = ?3. (2) log(3x ? 2) = 2. (3) 2 log x
Properties of Logarithms.pdf
Worksheet by Kuta Software LLC. Condense each expression to a single logarithm. 13) log 3 ? log 8. 14) log 6. 3. 15) 4log 3 ? 4log 8. 16) log 2 + log 11 +
Logarithms
explain what is meant by a logarithm. • state and use the laws of logarithms. • solve simple equations requiring the use of logarithms. Contents.
Worksheet 2.7 Logarithms and Exponentials
The mathematics of logarithms and exponentials occurs naturally in many branches of science. Use the logarithm laws to simplify the following:.
MATHEMATICS 0110A CHANGE OF BASE Suppose that we have
(loga a = 1 is one of the laws of logarithms.) So we see that. Special Case Formula: logb a = 1 loga b. Example 3. Express log e as a natural logarithm.
LOGARITHMS
Evaluate the solution to logarithmic equations to find extraneous roots. 11.0 Students prove simple laws of logarithms.
Download Free Geometric Mean Worksheet Answers (PDF
Solve Coulomb's Law quick study guide PDF worksheet 6 trivia questions bank: Charge is factorization
The laws of logarithms
The laws of logarithms. There are a number of rules which enable us to rewrite expressions involving logarithms in different yet equivalent
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) 13 logx+13 logy (8) logx+12 logz (9) 13 (logxlogylogz) (10) 14 logx+12 logylogz (11) 54
logx12 logz (12) 12 logx+ logy4logz
4. (1) 3
4= 81 (2) 7 1= 7 (3) 12 3 =18 (4) 3 0= 1 (5) 4 3=164 (6) 6 2=136 (7)xz=y (8)m12 =n5. (1) log
864 = 2
(2) log1010000 = 3
(3) log 4116=2 (4) log 3181
=4 (5) log 12 32 =5
(6) log 13 27 =3
(7) log xy= 2z (8) log xy=126. (1) True (2) False (3) True (4) False (5) False (6) False (7) True (8) True
7. (1)S=fe3g
(2)S=f34g (3)S=f2;4g (4)S=f5g (5)S=f2g (6)S=f6g (7)S=f5g (8)S=f3g8. (1)
log pb x= 2logbx log pb x=logxlog pb logx1 2 logb = 2 logxlogb = 2log bx(2) log 1pb px=logbx log 1pb px=logpx log 1pb 12 logx 12 logb =logxlogb =logbx(3) log b4x2= logbpx log b4x2=logx2logb42logx4logb
12 logxlogb 12 logbx = log bpx9. (1) 2x+y (2)x+ 2 (3)xy+z (4)y1 (5)yx (6)y+zx (7) 1x+y (8)x+yz+ 310. (1)S=f2:402g
(2)S=f0:369g (3)S=f7:213g (4)S=f0:438g (5)S=f1:652g (6)S=fln4g (7)S=flog54g (8)S=fln5g11. (1)
Dom(f) =]0;+1[
R(f) =R
Zeros: 1
Y-intercept: None
Variation:
f(x)%ifx2]0;+1[ f(x)&ifx2 ;Extremums: Max: None, Min: None
Sign: f(x)0 ifx2]0;1] f(x)0 ifx2[1;+1[(2)Dom(f) =] 1;0[R(f) =R
Zeros:1
Y-intercept: None
Variation:
f(x)%ifx2 ; f(x)&ifx2] 1;0[Extremums: Max: None, Min: None
Sign: f(x)0 ifx2] 1;1] f(x)0 ifx2[1;0[ (3)Dom(f) =]3;+1[
R(f) =R
Zeros: 4
Y-intercept: None
Variation:
f(x)%ifx2 ; f(x)&ifx2]3;+1[Extremums: Max: None, Min: None
Sign: f(x)0 ifx2]3;4] f(x)0 ifx2[4;+1[(4)Dom(f) =] 1;3[R(f) =R
Zeros: 2
Y-intercept:2
Variation:
f(x)%ifx2] 1;3[ f(x)&ifx2 ;Extremums: Max: None, Min: None
Sign: f(x)0 ifx2]2;3[ f(x)0 ifx2] 1;2[ (5)Dom(f) =]1;+1[
R(f) =R
Zeros: 0
Y-intercept: 0
Variation:
f(x)%ifx2 ; f(x)&ifx2]1;+1[Extremums: Max: None, Min: None
Sign: f(x)0 ifx2]1;0[ f(x)0 ifx2]0;+1[(6)Dom(f) = ]3;+1[R(f) =R
Zeros:1
Y-intercept: 2ln32
Variation:
f(x)%ifx2]3;+1[ f(x)&ifx2 ;Extremums: Max: None, Min: None
Sign: f(x)0 ifx2[1;+1[ f(x)0 ifx2]3;1] (7)Dom(f) =]2;+1[
R(f) =R
Zeros:1:5
Y-intercept: ln4
Variation:
f(x)%ifx2]2;+1[ f(x)&ifx2 ;Extremums: Max: None, Min: None
Sign: f(x)0 ifx2[1:5;+1[ f(x)0 ifx2]2;1:5](8)Dom(f) =] 1;2[R(f) =R
Zeros:53
Y-intercept:2ln6
Variation:
f(x)%ifx2] 1;2[ f(x)&ifx2 ;Extremums: Max: None, Min: None
Sign: f(x)0 ifx2[53 ;2[ f(x)0 ifx2] 1;5312. (1)f1(x) = 2x+5+ 3
(2)f1(x) = 3x13 3 (3)f1(x) =12 102x2+ 1 (4)f1(x) =12 e1x+12 (5)f1(x) = log2(x+ 3) (6)f1(x) =13 log3x+ 12 (7)f1(x) =ln2x5 (8)f1(x) =12 ln1x2
13. 37 years.
14. 9 years.
15. 53 years old.
16. (a)f(t) = 1000021:5t. Wheretis
the number of hours. (b) 28 284 bacteria. (c) 92.88 minutes.quotesdbs_dbs6.pdfusesText_12[PDF] laws of new york
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