# Logarithm

Worksheet 6 Name:

Problems 1-2. Determine if the function is exponential. If so then determine the growth/decay

factor.

1) 4( ) 3h x x 2)

1 ( ) 3

3

x

f x  

    

Problems 3-6. Sketch the graph. Make sure to label at least three points and the horizontal

asymptote.

3) ( ) 3 xf x  4)

1 ( )

2

x

g x  

    

5) 2( ) 2 3xf x    6)

3( ) 2 2xf x  

Problems 7-10. Sketch the graph. Make sure to label at least three points and the vertical asymptote.

7) 3( ) log ( )f x x 8) 2( ) log (3 )g x x 

9) 2( ) log ( 3) 2f x x    10) 2( ) log (1 ) 4f x x   

Problems 11-16. Write the logarithm in exponential form.

11) log ( ) 3b x  12) ln(5) 8 2x   13) 5log( ) 2 127x  

14) 4log ( 7) 8 2x    15) 92log ( 2) 9x   16) 23log( 2) 1 13x   

Problems 17-22. Write the exponential in logarithmic form.

17) 3 11 xe   18)

51.3 x 19) 4 7

2

x y

 

20) 92.3 7x  21)

310 1 3

2

x   22)

3 5 7xe z  

Problems 23-26. Simplify.

23) 3log (9) 24) 700

7log (49 ) 25) 2 1

2 log ( ) 3 4

 26) 7

1 ln

e

     

Problems 27-30. Determine the domain and range of the function. Write in interval notation.

27) 1( ) 2 2xf x   28) ( ) ln( 3) 4g x x  

29) 1( ) 3 4xf x    30) 2( ) log ( 2) 3h x x  

31) Find the amount after 3 years if \$1000 is invested at an interest rate of 12% per year, compounded

continuously.

32) A sum of \$1200 is invested at an interest rate of 7.5% per year. Find the amount in the account after 4

years if interest is compounded monthly.

Problem 33. Expand the logarithm. (2 points)

33) 3 7

5 2 log

9 ( 3)

x

x x

     

Problem 34. Combine. Write as a single logarithm. (2 points)

34) 1

ln(3) 5ln( 3) ln( 1) 3ln( ) 5ln( ) 3

x x x x      

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