Worksheet: Logarithmic Function PDF

Worksheet: Logarithmic Function

Write the following equalities in exponential form. (1) log3 81 = 4. (2) log7 7 = 1. (3) log1. 2.

Logarithmic Equations.pdf

Worksheet by Kuta Software LLC. Kuta Software - Infinite Algebra 2. Name___________________________________. Period____. Date________________. Logarithmic

Worksheet 2.7 Logarithms and Exponentials

Logs have some very useful properties which follow from their definition and the equivalence of the logarithmic form and exponential form. Some useful

Infinite Precalculus - Exponents and Logarithms

. Worksheet by Kuta Software LLC. Kuta Software - Infinite Precalculus. Exponents and Logarithms Rewrite each equation in logarithmic form. 13) x y = 178. 14 ...

Integrals Involving Exponential and Logarithmic Functions

In this section we explore integration involving exponential and logarithmic functions. Integrals of Exponential Functions. The exponential function is perhaps

Exponential and logarithmic functions

The module Indices and logarithms (Years 9–10) covered many properties of exponential and logarithmic functions including the index and logarithm laws. Now

Derivatives of Exponential and Logarithmic Functions. Logarithmic

Derivatives of Exponential and Logarithmic Functions. Logarithmic Differentiation. Derivative of exponential functions. The natural exponential function can

Math 120 - Review Sheet Exponential and Logorithmic Functions

Worksheet by Kuta Software LLC. Rewrite each equation in logarithmic form. 16) 4. 2. = 16. 17) x. −4. = y. 18) m. 3. = n. 19) 12 x. = y. 20) a. −7. = b. Find

Infinite Algebra 2 - Solving Exponential and Logarithmic Equations

. Worksheet by Kuta Software LLC. -2-. Solve each equation. Round your answers to the nearest ten-thousandth. 11) 4 x. = 72. 12) e b - 2. = 12. 13) e r. - 7 =

Unit 8: Exponential & Logarithmic Functions

Worksheet. 13. Review. 14. Test. Date ______. Period_________. Unit 8: Exponential & Logarithmic Functions. Page 2. Objective: To model exponential growth.

Worksheet: Logarithmic Function

Write the following equalities in exponential form. (1) log3 81 = 4. (2) log7 7 = 1. (3) log1. 2.

derivative-of-exponential-and-logarithmic-functions.pdf

If you are not familiar with exponential and logarithmic functions you may wish to consult the booklet Exponents and Logarithms which is available from the

Worksheet 2.7 Logarithms and Exponentials

Logs have some very useful properties which follow from their definition and the equivalence of the logarithmic form and exponential form. Some useful

Higher Mathematics EXPONENTIALS & LOGARITHMS

4 Exponentials and Logarithms to the Base e. EF 6. 5 Exponential and Logarithmic Equations Remember that the graph of an exponential function ( ).

Indiana Landmarks

Write an example below to some of exponents worksheet functions showing Exponential functions date either Work logarithmic function. Algebra worksheets ...

Unit 8: Exponential & Logarithmic Functions

8.5 Exponential and Logarithmic. Equations Applications of Natural Logs. Worksheet ... B. An exponential function is a function with the general form ...

Exponential and Logarithmic Graph Worksheet

Graphing Exponential and Logarithmic Functions. Name: Graph the following Exponential Functions. 1. 3. 2. 1 x y. +. = -. 2. 2. 4. 3. 1. 3 x y. -. ? ?. = +.

Comparing Exponential and Logarithmic Rules

Task 1: Looking closely at exponential and logarithmic patterns… 1) In a prior lesson you graphed and then compared an exponential function with a

6.5 Applications of Exponential and Logarithmic Functions

Equations 6.2 and 6.3 both use exponential functions to describe the growth of an investment. Curiously enough the same principles which govern compound

Limits of exponential and logarithmic functions worksheet

Limits of exponential logarithmic and trigonometric functions worksheet. Applying the natural logarithm function to both sides of the equation ...

Vanier College Sec V Mathematics

Department of Mathematics 201-015-50Worksheet: Logarithmic Function

1. Find the value ofy.

(1) log

525 =y(2) log31 =y(3) log164 =y(4) log218

=y (5) log

51 =y(6) log28 =y(7) log717

=y(8) log319 =y (9) log y32 = 5 (10) log9y=12 (11) log418 =y(12) log9181 =y

2. Evaluate.

(1) log

31 (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 2z

4(4) logxyz

(5) log xyz (6) logxy 2 (7) log(xy)13 (8) logxpz (9) log 3px 3 pyz (10) log4rx 3y2z

4(11) logxrpx

z (12) logrxy 2z 8

4. Write the following equalities in exponential form.

(1) log

381 = 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) 8

2= 64 (2) 103= 10000 (3) 42=116

(4) 34=181 (5) 12 5 = 32 (6)13 3 = 27 (7)x2z=y(8)px=y

6. 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= 2k

7. Solve the following logarithmic equations.

(1) lnx=3 (2) log(3x2) = 2 (3) 2logx= log2 + log(3x4) (4) logx+ log(x1) = log(4x) (5) log

3(x+ 25)log3(x1) = 3 (6) log9(x5) + log9(x+ 3) = 1

(7) logx+ log(x3) = 1 (8) log2(x2) + log2(x+ 1) = 2

8. Prove the following statements.

(1) log pb x= 2logbx(2) log1pb px=logbx(3) logb4x2= logbpx

9. 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) 3

2x+1= 2x2(6)101 +ex= 2

(7) 5

2x5x12 = 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) = 12e2x

13. 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)2

2. (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 =n

5. (1) log

864 = 2

(2) log

1010000 = 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=f3g

8. (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=logx2logb4

2logx4logb

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+ 3

10. (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=fln5g

11. (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;53

12. (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) =12quotesdbs_dbs11.pdfusesText_17

[PDF] Worksheet: Logarithmic Function

Vanier College Sec V Mathematics

1. Find the value ofy.

525 =y(2) log31 =y(3) log164 =y(4) log218

51 =y(6) log28 =y(7) log717

2. Evaluate.

31 (2) log44 (3) log773(4)blogb3(3) log2553(4) 16log48

3. Write the following expressions in terms of logs ofx,yandz.

4(4) logxyz

4(11) logxrpx

4. Write the following equalities in exponential form.

381 = 4 (2) log77 = 1 (3) log12

5. Write the following equalities in logarithmic form.

2= 64 (2) 103= 10000 (3) 42=116

6. True or False?

7. Solve the following logarithmic equations.

3(x+ 25)log3(x1) = 3 (6) log9(x5) + log9(x+ 3) = 1

8. Prove the following statements.

9. Given that log2 =x, log3 =yand log7 =z, express the following expressions

10. Solve the following equations.

2x+1= 2x2(6)101 +ex= 2

2x5x12 = 0 (8)e2x2ex= 15

11. Draw the graph of each of the following logarithmic functions, and analyze each

12. Find the inverse of each of the following functions.

13. 15 000$ is invested in an account that yeilds 5% interest per year. After how

14. 8 000$ is invested in an account that yeilds 6% interest per year. After how

15. Starting at the age of 40, an average man loses 5% of his hair every year. At

16. A bacteria culture starts with 10 00 bacteria and the number doubles every 40

ANSWERS

1. (1) 2

2. (1) 0

4. (1) 3

5. (1) log

864 = 2

1010000 = 3

7. (1)S=fe3g

8. (1)

2logx4logb

10. (1)S=f2:402g

11. (1)

Dom(f) =]0;+1[

R(f) =R

Zeros: 1

Y-intercept: None

Variation:

Extremums: Max: None, Min: None

R(f) =R

Zeros:1

Y-intercept: None

Variation:

Extremums: Max: None, Min: None

Dom(f) =]3;+1[

R(f) =R

Zeros: 4

Y-intercept: None

Variation:

Extremums: Max: None, Min: None

R(f) =R

Zeros: 2

Y-intercept:2

Variation:

Extremums: Max: None, Min: None

Dom(f) =]1;+1[

R(f) =R

Zeros: 0

Y-intercept: 0

Variation:

Extremums: Max: None, Min: None

R(f) =R

Zeros:1

Y-intercept: 2ln32

Variation:

Extremums: Max: None, Min: None

Dom(f) =]2;+1[

R(f) =R

Zeros:1:5

Y-intercept: ln4

Variation:

Extremums: Max: None, Min: None

R(f) =R