Intermediate Algebra (11th edition)

SECTION 10.3 Logarithmic Functions 593

27.Match each logarithm in Column I with
its value in Column II. See Example 3.
III
(a) A.
(b) B. 0
(c) C. 1
(d) D.0.1

28.When a student asked his teacher to

explain how to evaluate

without showing any work, his teacher

told him, “Think radically.” Explain

what the teacher meant by this hint.

log 9 3

log 2727

log0.3 1

log 16 1

log 8 8 - 1

Solve each equation. See Examples 2 and 3.

29. 
    
    
    
    30. 
        
        
        
        31. 
            
            
            
            32. 
                
            
            
            
            
        
        
        
        
    
    
    
    


30. 
    
    
    
    34. 
        
        
        
        35. 
            
            
            
            36. 
                
            
            
            
            
        
        
        
        
    
    
    
    


31. 
    
    
    
    38. 
        
        
        
        39. 
            
        
        
        
        
    
    
    
    

40. 41. 42.

43. 44. 45.

46.log 4264 =x 47.log 4 12 x+ 42 = 3 48.log 3 12 x+ 72 = 4

logp p^4 =x log 22 A (^22) B^9 =x log 62216 =x
logx log 8 32 =x log 81 27 =x

1

10

=- 1

logx

1

25

logx x= 1 logx 1 = 0 =- 2

logx 125 =- 3 logx 64 =- 6 log 12 x= 0 log 4 x= 0

logx 5 =

1

2

logx 9 =

1

2

x=log 27 3 x=log 125 5

Write in exponential form. See Example 1.

15. 
    
    
    
    16. 
        
        
        
        17. 
            
        
        
        
        
    
    
    
    


16. 
    
    
    
    19. 
        
        
        
        20. 
            
        
        
        
        
    
    
    
    


17. 
    
    
    
    22. 
        
        
        
        23. 
            
        
        
        
        
    
    
    
    

24.log1/8 25.log 5 5 -^1 =- 1 26.log 10 10 -^2 =- 2

1

2

=

1

3

log1/4

1

2

=

1

2

log 64 2 =

1

6

log 9 3 =

1

2

log 100 100 = 1 log 6 1 = 0 logp 1 = 0

log 10

1

10,000

log 4 64 = 3 log 2 512 = 9 =- 4

If is on the graph of (for and ),then is on the graph
of. Use this fact, and refer to the graphs required in Exercises 5– 8in Sec-
tion 10.2to graph each logarithmic function. See Examples 4 and 5.

49. 
    
    
    
    50. 
        
        
        
        51. 
            
            
            
            52. 
                
            
            
            
            
        
        
        
        
    
    
    
    

53.Explain why 1 is not allowed as a base for a logarithmic function.

54.Compare the summary of facts about the graph of in Section 10.2with the
similar summary of facts about the graph of in this section. Make a list of
the facts that reinforce the concept that ƒ and gare inverse functions.

55.Concept Check The domain of is while the range is. There-

fore, since defines the inverse of ƒ, the domain of gis , while

the range of gis.

56.Concept Check The graphs of both and rise from left to right.
Which one rises at a faster rate?

ƒ 1 x 2 = 3 x g 1 x 2 =log 3 x

g 1 x 2 =loga x

ƒ 1 x 2 =ax 1 - q, q 2 , 1 0, q 2

g 1 x 2 =loga x

ƒ 1 x 2 =ax

y=log 3 x y=log 5 x y=log1/3 x y=log1/5 x

ƒ-^11 x 2 =loga x

1 p, q 2 ƒ 1 x 2 =ax a 70 aZ 1 1 q, p 2

Concept Check Use the graph at the right to predict the
value of for the given value of t.

57. 
    
    
    
    58. 
        
        
        
        59. 
            
        
        
        
        
    
    
    
    

60.Show that the points determined in Exercises 57– 59lie on
the graph of ƒ 1 t 2 =8 log 5 12 t+ 52.

t= 0 t= 10 t= 60

ƒ 1 t 2

f(t)

t

16

24

8

0 5 60