3.3 The Natural Logarithmic Function: Exercises

1.   Without using a calculator, find each of the following:

      a)                        

     b)                      

c)                

d)   

      e)                      

    f)                     

g)           

h)   

2.  Without using a calculator, find each of the following:

      a)                        

b)                     

c)    

3.  Write each of the following in exponential form:

     a)               

b)                            

c)   

     d)                  

e)                         

f)    

4.  Write each of the following as a logarithmic equation:

     a)                        

b)                                

5.  Write each of the following as a logarithmic equation, then solve for x:

     a)                      

b)                                   

c)   

d)   

6.   Find

            a)                          

b)                                     

c)   

 7.  Find

            a)                                                                       

b)   

c)   

8.    Evaluate    

           a)                           

b)   

9.   a)   What is the domain and range of  ?  What is the asymptote of its graph?

      b)   What is the domain and range of  ?  What is the asymptote of its graph?

10.   Immediately following the gold medal performance of the US women’s gymnastic     

       team in the 1996 Olympic Games, and NBC commentator said of one of the team     

       members:  “Her confidence and performance have grown logarithmically.”  He         

       clearly thought this was a wonderful compliment.  Is it a compliment?  *

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ANSWERS TO ODD NUMBERED PROBLEMS

DETAILED SOLUTIONS

*from Connally, Hughes-Hallett,  Gleason et al. (2000).   FUNCTIONS MODELING CHANGE.  A Preparation for Calculus.  New York:  John Wiley & Sons, p. 138