Algebra 2 - Chapter 8 Test Review

Algebra 2 - Chapter 8 Test Review
How is each graph translated from its parent graph?
1. y = 5| x – 4| + 7
2. y = 6(x +9)3 – 5
3. Write the following in logarithmic form: 3 –5 = 1/243
_________________
4. Write the following in exponential form: log 4 64  3
________________
Evaluate without a calculator:
6. log100
5. log5 5
7. log 9 √9
Evaluate: You must show steps as if you have NO calculator.
8. log 7 7 3 _______
9. log16
1
_______
4
1
10. 3 log9 3  log9 27 . ________
3
7𝑥
11. Expand: log 3 (𝑦 4 )
12. Your brain cells increase 15% per hour in math class. If you have 135 million brain
cells, write a function and then find how many million cells you have after 4 ½ hours
in math class. When will you have over 550 million brain cells?
13. How long would it take for $500 to double if it was invested at 4% interest
compounded continuously?
14. $1,500 is deposited into an account that pays 2.5% interest. Find the amount in the
account after 15 years if the interest is compounded
a) Monthly.
b) continuously.
Use properties of logarithms to evaluate: (no calculator)
15. log200 – log2
16. 3 log 4 2  2 log 4 2  log 4 2
Solve: You must clearly show each step. Please circle your answer.
5
17. 2 x 3  64
20. ex + 2 = 10
18. 2a–1 = 15
19. 23x = 120
23. ln( x  3)  ln x  1
21. log(3x + 5) = 11
24. ln5 + lnx = 3
22. ln (2x – 1) = 5
25. logx = –2
Use the following for 26 and 27:
log 𝑏 5 = .1234
26. log 𝑏 125
log 𝑏 𝑐 = .2468
27. log 𝑐 5
Solutions:
1. Right 4, up 7
2. Left 9, down 5
1
3. log3
 5
243
4. 4 3  64
5. 1
6. 2
1
7. 2
8. 3
1
9. − 2
10. 1
11. log 3 7 + log 3 𝑥 − 4log 3 𝑦
12. y  135(1.15) x , 253.2060 mil, 10
years
13. 27.73 years
14. a. $2181.64
b. $2182.49
15. 2
16. 3
17. 8
18. 4.9069
19. 2.3023
20. 0.3026
21. 3.3  1010
22. 74.7066
23. 3.7290
24. 4.0171
1
25.
100
26. 0.3702
1
27. 2