Intermediate Algebra (11th edition)

602 CHAPTER 10 Inverse, Exponential, and Logarithmic Functions

Complete solution available
on the Video Resources on DVD

10.4 EXERCISES

Use the indicated rule of logarithms to complete each equation. See Examples 1– 4.

1. ( product rule)


2. (quotient rule)


3. (special property)


4. ( power rule)


5. (special property)
   6.Evaluate. Then evaluate. Are the results the same? How
   could you change the operation in the first expression to make the two expressions
   equal?

Use the properties of logarithms to express each logarithm as a sum or difference of loga-

rithms, or as a single number if possible. Assume that all variables represent positive real

numbers. See Examples 1– 5.

7. 
   
   
   
   8. 
      
      
      
      9. 
         
      
      
      
      
   
   
   
   

10. 11. 12.

13. 14. 15.

16. 17. 18.

19.Concept Check A student erroneously wrote. When

his teacher explained that this was indeed wrong, the student claimed that he had used the

distributive property. WHAT WENT WRONG?

20.Write a few sentences explaining how the rules for multiplying and dividing powers of the

same base are similar to the rules for finding logarithms of products and quotients.

Use the properties of logarithms to write each expression as a single logarithm. Assume that

all variables are defined in such a way that the variable expressions are positive, and bases

are positive numbers not equal to 1. See Examples 1–5.

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22. 
    
    
    
    24. 
        
    
    
    
    


23. 
    
    
    
    26. 
        
    
    
    
    

27. 28.

29. 30.

31.

32.

1

3

logb x+

2

3

logb y-

3

4

logb s-

2

3

logb t

3 logp x+

1

2

logp y-

3

2

logp z-3 logp a

log 10 1 x+ 32 +log 10 1 x- 32 log 10 1 x+ 42 +log 10 1 x- 42

3 loga 5 -

1

2

3 loga 5 - 4 loga 3 loga 9

1 loga r-loga s 2 +3 loga t 1 loga p-loga q 2 +2 loga r

loga m-loga n logb x-logb y

logb x+logb y logb w+logb z

loga 1 x+y 2 =loga x+loga y

log 4

24 z# 25 w

s^2

log 2

23 x# 25 y

r^2

log 6

B

pq

7

log 3

B

xy

5

log 7

2313

pq^2

234

x^2 y

log 3

log 3 log 4 62 log 5 74

7

5

log 5

8

3

log 7 14 # 52 log 8 19 # 112

log 2 18 + 82 log 2 8 +log 2 8

log 3 39 =

log 10 36 =

3 log^3 4 =

log 10

7

8

=

log 10 17 # 82 =