Please do question 23, 25, 55, and 65

In s SECTION 5.5 Properties of Logarithms 315 In 2 5.5 Assess Your Understanding n 5 Concepts and Vocabulary - 2.3219 1. 10ga 1 = 2. alo& M = 9. True or False log2 (3x4) = 4 log2(3x) 3 . 10 ga d' = 10. True or False log(3) log 2 4. 10ga (MN) = log 3 11. Choose the expression equivalent to 2t . 10ga N (a) e2x (b) et In 2 (c) e log 2x (d) e2 In x 12. Writing log ax - logay + 210gaz as a single logarithm ic functions 6. 10ga M' = results in which of the following? log5 7 7. If log & M = logs 8' . then M = (a) log a (x - y + 2z) (b) log a ) Nor e 8. True or False In (x + 3) - In (2x) = - In (x + 3) In (2x) (c) log . (2x2 ) (d) log a (vz z) f logarithms Skill Building he graph of Problems 13-28, use properties of logarithms to find the exact value of each expression. Do not use a calculator. 13. log3 371 14. log2 2-13 15. Ine 4 16. In e V2 y graphing 17. 21082 18. eln 8 19. log: 2 + log8 4 20. log6 9 + 10g6 4 21. logo 18 - 10g6 3 22. logg 16 - logg 2 23. log2 6 . log6 8 24. log3 8 . log8 9 25. 31083 5-1083 4 26. 51085 6+1085 7 27. e log 2 16 28. @10829 In Problems 29-36, suppose that In 2 = a and In 3 = b. Use properties of logarithms to write each logarithm in terms of a and b. 29. In 6 30. In 31. In 1.5 32. In 0.5 33. In 8 34. In 27 35. In V6 36. In 1/2 0. In Problems 37-56, write each expression as a sum and/or difference of logarithms. Express powers as factors. 37. logs (25x) 38. log3 9 39. log2 23 40. log7 x5 41. In (ex) 42. In- 44. In (xet) 45. loga (uv' ) u > 0, v > o 46. 10g2 72) a > 0 , b > o 47. In (x2 V1 - x) 0 0 49. log2 ) * > 3 50. logs - (V x + 1 x 2 - 1 x > 1 51. log - [x(x + 2) 7 XVx+ 1 1 12 - x - 2 1/3 L ( x + 3) 2_ x 2 0 52. 108 (x - 2)2 x > 2 53. In L ( x + 4) 2 x > 2 In ( x - 4 ) 272/3 x2 - 1 . * > 4 55. In 5x V1 + 3x x > 4 1 5x2 V 1 - x ( x - 4) 3 56. In 4 ( x + 1 ) 2 0