Please answer the following questions #42, 44, 48, 52, 54, 56, 58, 64, 68

Do exercises, following the same exact format from the examples that are going to be provided.

Questions:

x 54. f(x) = In (In 3x) 55. f(x) = In X x2 + 5 56. f(x) = In 57. f(x) = ex In x X 58. S(x) = e2x In x 59. S(x) = ex sec x 60. S(x) = (sin 2x)e* 61. S(x) = In (e* + 1) 62. f(x) = In (ex - 2) 63. S(x) = (In x)2 64. S(x) = (In x)3 65. y = (In x) -4 66. y = (In x)" 67. f(t) = In (13 + 1)5 68. f(t) = In (12 + 1)3 69. S(x) = [In (x + 5)]4calculator Solve for T write In (0 . 00 ) /- 0.02 35) et = 100 41 1 ) e-0. 021 = 0.06 Loge 100 = T Base - e In 10o = T exponent = - 0. 027 T = 4. 605170 Loge 0.06 =+ 0.0271 - 8. 02 - 0/027 Differentiate T= In0. 06 43 ) y = - 6 Inx 1 - 0.02 T= 140. 670536 d Inx = 1 j d Inf (x ) = f ( x ) dx dx F( y ) cly = - 6 ( # ) = 6 dx X oct 45 ) 1 = * " Inx -1 * 2 2 - > f = X 4 ( ) = 41 X 3 --simplify " = (# ) do = (x 3 ( inx + x " ( * ) - X 1 ( 2 X) = - X 4 x 3 / n x + * 3 _ x 2Find the logarithm. Round to six decimal places. 29. In 3927 30. In 12,000 31. In 0.0182 32. In 0.00087 33. In 8100 34. In 0.011 Solve for t. 35. e' = 100 36. e' = 1000 37. e' = 60 38. e' = 90 39. e- = 0.1 40. e-' = 0.01 41. e-0.021 = 0.06 42. e0.071 = 2 Differentiate. 43. y = -6 In x 44. y = -4 10 x 45. y = x" Inx - 3x2 46. y = x' Inx - 4x4 In x In x 47 . y = x 48. y =$5 49. y = In Hint: In In x - In 4. 4 50. y = In X 2 51. g(x) = In cos x 52. g(x) = In tan x 53. f(x) = In (In 4x)