Math 3- Unit 4 Test Review – Exponential and Logarithmic Functions
Name: ______________________________
Directions: Show all work for each problem.
Write in Logarithmic Form:
1. 5−2 =
1
25
2. 43 = 64
3. 83 = 512
Write in Exponential Form:
4. log 2 64 = 6
1
1
5. log 4 = −1
6. log
7. log 3 27 = 𝑥
8. log 𝑥 81 = 2
9. log 2 𝑥 = −4
10. log 5 125 = 𝑥
11. log 𝑥 216 = 3
12. log 25 𝑥 =
4
100
= −2
Solve each logarithmic equation:
1
2
Evaluate each logarithmic expression. Round to nearest hundredth
13. log 4 156
14. log 2 45
15. log11 323
17. 𝑒 𝑥 = 15
18. ln(𝑥 − 2) = 2
Evaluate each natural logarithmic expression:
16. 𝑒 ln 5𝑥 = 20
19. 𝑒 3𝑥 = 30
20. 2𝑒 𝑥 − 1 = 11
21. 4 ln 𝑥 = −2
Identify the domain and range of each. Then sketch the graph.
22. 𝑦 = log 6 (𝑥 − 1) − 5
23. 𝑦 = log 5 (𝑥 − 1) + 3
24. 𝑦 = 𝑒 𝑥 − 6
Write an exponential function to model each situation. Find each amount after the specified time.
25. A new car that sells for $22,000 depreciates 23% each year for 5 years.
26. The price of a new home is $225,000. The value of the home appreciates 1.5% each year. How much will
the home be worth in 20 years?
27. If Mark deposits $12,000 in a savings account paying 2.4% interest compounded daily, what is the balance
in the account after 8 years?
28. How much would Mark have if the interest was compounded weekly?
29. In 2009, there were 1570 bears in a wildlife refuge. In 2010, the population had increased to
approximately 1884 bears. If this trend continues and the bear population is increasing exponentially, how
many bears will there be in 2018?
30. A compound decays according to the equation 𝑦 = 𝑎𝑒−.0536𝑡, where 𝑡 is in days. Find the half-life of the
compound. Round to the nearest hundredth.
Describe the translations. Use words left, right, up, down and tell how many.
31. Comparing to y
x , how does the graph of y
x
32. Comparing to y
3 x , how does the graph of y
33. Comparing to y
log x , how does the graph of y
8 shift? ______________________________
3 x 7 shift? ______________________________
log( x 6) 1 shift? ____________________________