Worksheet 6 Name:
Problems 1-2. Determine if the function is exponential. If so then determine the growth/decay
1) 4( ) 3h x x 2)
1 ( ) 3
Problems 3-6. Sketch the graph. Make sure to label at least three points and the horizontal
3) ( ) 3 xf x 4)
1 ( )
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
20) 92.3 7x 21)
310 1 3
3 5 7xe z
Problems 23-26. Simplify.
23) 3log (9) 24) 700
7log (49 ) 25) 2 1
2 log ( ) 3 4
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
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)
Problem 34. Combine. Write as a single logarithm. (2 points)
ln(3) 5ln( 3) ln( 1) 3ln( ) 5ln( ) 3
x x x x
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