Name:_________________________________ Date:__________ Period:__________
Algebra 2 Ch.8 Test
Evaluate each function to the nearest hundredth for x = -2, -1, 0, 1, and 2.
Use a Table and Graph each function.
1. y

3 ( 2 ) x 2. y

1
2
( 4 ) x
Write an exponential function of the form y
 ab x
that includes the given points.
3. (1, 2), (2, 8) 4. (2, 122.5), (3, 857.5)
5. You put $2000 into an account earning 4% interest compounded continuously.
Find the amount at the end of the 8 th
yr.
Describe how the graph of each function is related to the graph of its parent function.
6. y
 
3 x

4 7. y

5 x

1 
2

Name:_________________________________ Date:__________ Period:__________
Use the Change of Base Formula to rewrite each expression using common logarithms (base 10).
8. log
4
12
Evaluate each logarithm .
9. log
2
8
13. log
9
1
3
10. log 125
5
11. log
1
2
1
4
12. log 729
3
Graph the logarithmic function.
Show the Inverse and Use a Table
14. y
 log
4 x
Inverse:___________
Write each equation in logarithmic form.
15. 7
3 
343 16. 2

4 
0 .
0625
Write each logarithmic expression as a single logarithm.
17. log 2

3 log 5 18. log a
 log ab
Expand each logarithm.
19. log
5
6 x 20. log
5 x
2 y z
4
Write each expression as a single natural logarithm.
21. 2 ln 10
 ln 5 22. 5 ln a

3 ln b

Name:_________________________________ Date:__________ Period:__________
Use the properties of logarithms to evaluate each expression.
23. log 5
 log 10
 log 2 24. log 4
8
 log
8
16
Solve each equation. Round to the nearest hundredth.
25. log 5 x

3 26. 10 2 x 
40
27. log
5
( 3 x

10 )

3 log
5
4

2 28. 8 x

1 
12
Use the properties of logarithms to simplify each equation and solve it. Round to the nearest hundredth.
29. ln( x

3 )

1 30. 2 ln x
 ln 3

2 31. e
3 x 
12
32. A parent raises a child’s allowance by 15% each year. If the allowance is $3 now, when will it reach $21?
33. Hg-197 is used in Kidney scans. It has a half-life of 64 hr.
Write the exponential decay function for a 12-mg sample. Find the amount remaining after 96 hr.