MAT146 Review Exam II Fall 2011 1 1. Solve: . a. b. c. d. 2. Which of the following is the graph of the logarithmic function 2( ) log 2?f x x a. b. c. d. 3. Solve: . a. b. c. d. 4. Find the exponential form of the logarithmic equation: 93log 27 .2 a. c. b. d. d. 5. Evaluate: . a. 10.407 b. 9.177 c. 12.723 d. 3.181 log75 14 3x  bg357575217353295xy xy xy xy 7501700ex– .07282728.– .06592639.32927FHGIKJ27 93 232279FHGIKJ9 273 2log2579MAT146 Review Exam II Fall 2011 2 6. What is the y-intercept of ( ) 1xf x e? a. (0,1) b. (0,0) c. (1,0) d. (- 1,0) 7. Solve: 0.062 39 39.4.xe a. b. c. -3.333 d. 8. Solve: . a. b. c. d. 9. Find the graph of the function . a. b. c. d. 10. Solve: . a. 1.056 b. 0.308 c. 38 d. 93.838 11. The number of bacteria present in a culture is , where t is the time in minutes. Find the time required, to the nearest half minute, to have 5000 bacteria present. a. 11.5 min. b. 10.5 min. c. 10.0 min d. 11.0 min 0572.11650.26824.12797 4x1251411114f xxbg 31xy xy xy xy 3 6 19ln xbgB et 10000146.MAT146 Review Exam II Fall 2011 3 12. Simplify completely as a sum and/or difference of logs. (Assume all variables are positive.) a. b. c. d. 13. Chemists measure the acidity of an aqueous solution using pH. The pH is, where pH is a measure of the hydrogen ion concentration measured in moles of hydrogen per liter of a solution. Find the pH of a solution if a. 10.8 b. 3.2 c. 10.2 d. 3.8 14. Find the time required for an investment of $7000 to double if the interest rate of 13% is compounded continuously. Use the formula rtA Pe. a. 2.67 years b. 5.33 years c. 10.66 years d. 3.55 years 15. Solve: . a. b. c. – 6 d. 6 16. Evaluate: . a. 16 b. 6 c. 16 d. – 6 17. Evaluate: . a. 2 b. c. d. logbx yz8 73216 14 6log log logb b bx y z 6logbx y z bg47232log log logb b bx y z 5632log loglogb bbx yzbgbgpH H log10HH .  17 104.1264FHGIKJx1616log642lne212e2e12MAT146 Review Exam II Fall 2011 4 18. Find the graph of the logarithmic function . a. b. c. d. 19. Evaluate: . a. 20 b. c. – 4 d. 20. The number of units sold for a certain product is , where t is the number of years after the product is introduced. What are the expected sales 2 years after the product is introduced? a. 4841 units b. 4849 units c. 6766 units d. 5822 units 21. On the Richter scale, the magnitude R of an earthquake of intensity I is, where is the minimum intensity used for comparison. Find the magnitude R of an earthquake if a. 7.1 b. 8.1 c. 8.2 d. 6.6 f x xbgbg  5 3lnxy xy xy xy log51625FHGIKJ12014N t= 2100 5 6ln bgRII log0I01I  13300 000, , .MAT146 Review Exam II Fall 2011 5 22. If $3500 is invested in a long-term trust fund with an interest rate of 10% compounded continuously, what is the amount of money in the account after 15 years? a. $15,685.91 b. $25,861.70 c. $14,620.37 d. $17,335.61 23. What is the domain of 4log ( 3)?yx a. (-∞,3) b. (-∞,+∞) c. [-3,+∞) d. (-3,+∞) 24. Where does the graph of 33xy  intersect the graph of y = 6? a. x = 2 b. x = 1 c. x = 0 d. The graphs do not intersect. 25. Evaluate: . a. 96.639 b. 2187.000 c. –24.249 d. 0.010 26. Express as a single logarithm: . a. b. c. d. 27. Evaluate: . a. –0.528 b. –0.137 c. –8.789 d. –2.285 28. Solve 193x a. 2 b. 2 c. 12 d.12 29. In 1997, the population of a country was estimated at 4 million. For any subsequent year the population in millions is , where t is the number of years since 1997. Estimate the population in 2012. a. 5,304,000 b. 5,255,000 c. 5,206,000 d. 5,403,000 30. Write as a single logarithm: . a. b. c. d. 31. What is the vertical asymptote of( ) 2 logf x x? a. x = 2 b. x = 0 c. y = 0 d. y = 1 32. If log 6 0.35,log 2 0.42, and log 4 0.13, findlog 24a a a a  . a. 0.48 c. 1.16 b. 0.20 d. It cannot be determined from the given information. 143log log8 838 34log81292log84log log8 838 34log872log813P tbgP tetbg2405 54 990 0208..log logd d20 7logd13logd140logd27logd207MAT146 Review Exam II Fall 2011 6 33. Solve: . a. b. c. d. –3.041 34. If (6, 2) is on the graph of logayx, what point must be on the graph ofxya ? a. (2, 6) b. (-6,-2) c. (-2,-6) d. (1/6,1/2) 35. Solve: . a. b. c. 9 d. 36. Write as a single log: . a. c. b. d. none of these 37. Solve: . a. 0.455 b. 16 c. 2.200 d. 0.0625 38. Evaluate: . a. b. 5 c. d. 39. Solve: 2 2 2log (3 2 ) log (2 ) log 3xx   . a. 3x  b. 12x  c. 2x  d. no solution 40. Write as a sum and/or difference of logs: . a. b. c. d. 2 94x x2922.5843.5ln lnx  9 0e99eln 94 3 610 10log logx x bglog10126x x bglog10436xx bg12610logxx log log3 35 4x x  bgln e55e1515elogb20271220 27log logb bbg1220 27log logb bbglog logb b20 27logb1220 27bgMAT146 Review Exam II Fall 2011 7 Key for Review Exam II Logs and Exponentials 1.d 21.a 2.b 22.a 3.d 23.d 4.d 24.b 5.b 25.d 6.b 26.a 7.d 27.a 8.d 28.d 9.a