[PDF] [PDF] Worksheet 27 Logarithms and Exponentials

[PDF] Worksheet: Logarithmic Function - Department of Mathematics

z8 Page 2 4 Write the following equalities in exponential form 7 Solve the following logarithmic equations (1) lnx = − 

[PDF] Exponential and Log Functions Worksheet

Exponential and Log Functions Worksheet Exponential Functions and Inverse of a Function 1 Find the inverse of ( ) 2 3 f x x = - 2 Find the inverse of 4

[PDF] Worksheet 27 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 properties  

[PDF] 11 Exponential and Logarithmic Functions Worksheet - MA 109

11 Exponential and Logarithmic Functions Worksheet Concepts: • Rules of The graph of an exponential function g(x) = ax is shown below Find a x y -2 -1 0

[PDF] Unit 5B Exponentials and Logarithms - State College Area School

I can apply my knowledge of exponential and logarithmic functions to solve new and non-routine CPAlg2 Worksheet LT1 Answers 1) $2329 89 2) $2330 65

[PDF] Math 120 - Review Sheet Exponential and Logorithmic Functions

Worksheet by Kuta Software LLC 10) 4log 8 7 + log 8 6 3 Rewrite each equation in exponential form 11) log 2 32 = 5 Find the inverse of each function

[PDF] Solving Exponential and Logarithmic Functions Worksheet In 1-9

Solving Exponential and Logarithmic Functions Worksheet In 1-9, solve each exponential equation Where necessary, give the exact value and then use

[PDF] Solving Exponential & Logarithmic Equations

Inverse Properties of Exponents and Logarithms Base a Natural Base e 1 2 ➢ Solving Exponential and Logarithmic Equations 1 To solve an exponential 

[PDF] 11 Exponential and Logarithmic Functions Worksheet

11 Exponential and Logarithmic Functions Worksheet Concepts: • Rules of The graph of an exponential function g(x) = ax is shown below Find a x y -2 -1 0

[PDF] Exponential and Logarithmic Functions Unit Length - Fort Smith

Worksheet #2: Natural Logarithm Base with Key Task: Solving an Base Equation Bacteria Growth with Teacher Commentary from IM 3 

[PDF] exponential fourier series coefficient calculator

[PDF] exponential fourier series for signal

[PDF] exponential fourier series in signals and systems pdf

[PDF] exponential fourier series of half wave rectified sine wave

[PDF] exponential fourier series of half wave rectifier

[PDF] exponential fourier series of square wave

[PDF] exponential function to log calculator

[PDF] exponential to log conversion calculator

[PDF] exponential to natural log calculator

[PDF] exponentielle de 0 7

[PDF] exponentielle de 0 valeur

[PDF] exponentielle de x u003d0

[PDF] exponentielle traduction en arabe

[PDF] exponents and logarithms worksheet

[PDF] exponents surds and logarithms pdf

Worksheet2:7LogarithmsandExponentials

Section1Logarithms

Denition:

meansthat ify=logbxthen x=by y=logbxandx=byareequivalentstatements.

Example1

:Iflog4x=2then x=42 x=16

Example2

:Wehave25=52.Thenlog525=2.

Example3

:Iflog9x=12then x=91 2 x=p 9 x=3

Example4:Iflog2y3=4then

y 3=24 y 3=16 y=163 y=48

Exercises:

1.Writethefollowinginexponentialform:

(a)log3x=9 (b)log28=x (c)log327=x(d)log4x=3 (e)log2y=5 (f)log5y=2

2.Writethefollowinginlogarithmform:

(a)y=34 (b)27=3x (c)m=42(d)y=35 (e)32=x5 (f)64=4x

3.Solvethefollowing:

(a)log3x=4 (b)logm81=4 (c)logx1000=3(d)log2x 2=5 (e)log3y=5 (f)log24x=5

Section2PropertiesofLogs

log bmn=logbm+logbn log bm n=logbmlogbn log bma=alogbm log bm=logbnifandonlyifm=n Page2

Example1

log bxy z=logbxylogbz =logbx+logbylogbz

Example2

log

55p=plog55

=p1 =p

Example3

log

2(8x)1

3=13log28x

1

3[log28+log2x]

1

3[3+log2x]

=1+1

3log2x

Example4

:Findxif

2logb5+1

2logb9logb3=logbx

log b52+logb91

2logb3=logbx

log b25+logb3logb3=logbx log b25=logbx x=25 Page3

Example5:

log 28x3

2y=log28x3log22y

=log28+log2x3[log22+log2y] =3+3log2x[1+log2y] =3+3log2x1log2y =2+3log2xlog2y

Exercises:

(a)log2xylog2x2 (b)log28x2 y+log22xy (c)log39xy2log327xy (d)log4(xy)3log4xy (e)log39x4log3(3x)2

2.Findxif:

(a)2logb4+logb5logb10=logbx (b)logb30logb52=logbx (c)logb8+logbx2=logbx (d)logb(x+2)logb4=logb3x (e)logb(x1)+logb3=logbx lnx=logex Page4 e y=xandlnx=y

Example1

:elogea=a

Example2

:ealogex=elogexa=xa

Example3

log ee2y=2ylogee =2y

Example4

:logex25=2logexloge5

Exercises:

1.Useyourcalculatortondthefollowing:

(a)ln1:4 (b)ln0:872 (c)ln6:43:8 10 (d)e0:62 (e)e3:8(f)(e0:24)2 (g)e1:4e0:8 (h)6e4:1 (i) e8:2 1068
(j)e2:4e6:1(8+ln2)

2.Simplifythefollowing

(a)logx2logxy+4logy (b)ln(8x)1

2+ln4x2ln(16x)12

(c)e6e6(d)12e76e2 (e)lne2 (f)ln(e2lne3) Page5

3.Findxineachofthefollowing:

(a)lnx=2:7 (b)ln(x+1)=1:86 (c)x=e9:8e7:6 (d)6:27=ex (e)4:12=e2x Page6

Exercises2.7LogarithmsandExponentials

1.Evaluate

(a)log101000 (b)log41 (c)log327 (d)log21 4 (e)logaax

2.Solveforx

(a)log4x=2 (b)log1 3x=4 (c)log10(2x+1)=2 (d)log264=x (e)logb81=4

3.(a)Useloglawstosolvelog3x=log37+log33.

i.log1024ii.log109

8iii.log10720

ittakeforthepopulationtoreachonemillion?

E=1:741019101:44M

Howmanyjouleswerereleased?

Page7

Answers2.7

Section1

1.(a)x=39

(b)8=2x(c)27=3x (d)x=43(e)y=25 (f)y=52

2.(a)4=log3y

(b)x=log327(c)2=log4m (d)5=log3y(e)5=logx32 (f)x=log464

3.(a)81

(b)3(c)10 (d)64(e)243 (f)8

Section2

1.(a)log2y

x (b)4+3log2x (c)log3y1(d)2log4(xy) (e)0

2.(a)8(b)6

5(c)18(d)211(e)112

Section3

1.(a)0.34

(b)0:14(c)0.89 (d)1.86(e)44.70 (f)1.62(g)9.03 (h)0.10(i)3.41 (j)4.65

2.(a)lnxy3

(b) 1

2ln8+2lnx(c)1

(d)2e5(e)2 (f)2+ln3

3.(a)14:88

(b)5:42(c)9.03 (d)1:84(e)0:71 Page8

Exercises2.7

1.(a)3(b)0(c)3(d)2(e)x

2.(a)16(b)1

81(c)49.5or992(d)6(e)3

3.(a)21

(b)2 (c)i.x+yii.2yxiii.2y+x+1

4.(a)4.6054months

Page9quotesdbs_dbs14.pdfusesText_20