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 = 125

2. 43 = 64 3. 83 = 512

Write in Exponential Form:

4. log2 64 = 6 5. log414

= −1 6. log 1100

= −2

Solve each logarithmic equation:

7. log3 27 = 𝑥 8. log𝑥 81 = 2 9. log2 𝑥 = −4

10. log5 125 = 𝑥 11. log𝑥 216 = 3 12. log25 𝑥 =12

Evaluate each logarithmic expression. Round to nearest hundredth

13. log4 156 14. log2 45 15. log11 323

Evaluate each natural logarithmic expression:

16. 𝑒ln 5𝑥 = 20 17. 𝑒𝑥 = 15 18. ln(𝑥 − 2) = 2

19. 𝑒3𝑥 = 30 20. 2𝑒𝑥 − 1 = 11 21. 4 ln 𝑥 = −2

Identify the domain and range of each. Then sketch the graph.

22. 𝑦 = log6(𝑥 − 1) − 5 23. 𝑦 = log5(𝑥 − 1) + 3

24. 𝑦 = 𝑒𝑥 − 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 xy , how does the graph of 8xy shift? ______________________________

32. Comparing to xy 3 , how does the graph of 73xy shift? ______________________________

33. Comparing to xy log , how does the graph of 1)6log( xy shift? ____________________________