1. We can unite bases! Now bases are same!

2. We can unite bases! Now bases are same!

4. Check (Remember: Back to Original)

5. We can unite bases! Now bases are same!

7. 8-4 Solving Logarithmic Equations and Inequalities

8. Attention Inequality log Domain first.

10. Reverse the direction when dividing by “minus” From domain before

11. Check 1 (Remember: Back to Original)

12. Attention Inequality log Domain first.

13. From domain:

14. Check 1.5 (Remember: Back to Original)

15. Attention Inequality log Domain first.

16. From domain:

17. We can unite bases!

18. Now bases are same!

19. Attention Inequality log Domain first.

20. From domain

21. Check 0 (Remember: Back to Original)

22. 8-5 Properties of Logarithms

25. Do Cross Multiply

30. Use MODE 5 3 a = 1, b= -4, c= -32

31. Check -4 (Remember: Back to Original) Undefined, so ignore -4

32. Check 8 only solution is 8

34. Use MODE 5 3 a = 1, b= -2, c= -3

35. Check 3 (Remember: Back to Original) 3.1699 = 3.1699

36. Check -1 (Remember: Back to Original) Undefined, so ignore -1 only solution is 3

39. Square root both sides

40. Check -5 (Remember: Back to Original)

41. Check 5 (Remember: Back to Original) The solutions are 5 and -5

42. Solve. Check your solution.

45. Check 12 (Remember: Back to Original)

46. Solve. Check your solution.

47. Do Cross Multiply

48. Use MODE 5 3 a = 1, b= -1, c= -6

49. Check 3 (Remember: Back to Original)

50. Check -2 (Remember: Back to Original) Undefined, so ignore -2 only solution is 3

52. Raise the powers

55. Raise the powers first!

58. 8-6 Common Logarithms

59. Express log 9 22 in terms of common logarithms. Then approximate its value to four decimal places. Common logarithm change to base 10

60. Express log 5 14 in terms of common logarithms. Then approximate its value to four decimal places. Common logarithm change to base 10

61. We can’t unite bases! So, “log” both sides!

62. Divide by 2log5 !!

63. We can’t unite bases! So, “log” both sides!

64. Divide by 3log4 !!

65. We can’t unite bases! So, “log” both sides! A.0.2375 B.1.1132 C.3.3398 D.43.2563 Do the calculations!

72. Solve. Round to four decimal places. We can’t unite bases! So give “log”

74. We change L.H.S to base “b”

75. Challenge Evaluate

76. 8-7 Natural Logarithms

77. Remember!

78. First isolate the “ln” then give it base “e”

81. First isolate the “e” then “ln” both sides

84. Write each exponential in logarithmic form “ln” both sides

85. Write each exponential in logarithmic form “ln” both sides

86. Write each logarithm in exponential form “e” both sides

87. Write each logarithm in exponential form “e” both sides

88. Write each expression as a single logarithm

90. Challenge Evaluate

91. Challenge Solve

93. Check -3 undefined Check 4

94. 7-1 Operations on Functions

95. We can unite bases! Now bases are same!

97. Compound Interest You deposited $700 into an account that pays an interest rate of 4.3% compounded monthly. How much will be in the account after 7 years?

99. Compound Interest You deposited $1000 into an account that pays an interest rate of 5% compounded quarterly. a) How much will be in the account after 5 years?

101. Compound Interest You deposited $1000 into an account that pays an annual rate of 5% compounded quarterly. b) How long it take until you have a $1500 in your account?

102. Divide both sides by 1000

103. “log” both sides now Divide both sides by 4log1.0125

105. X Y -2 3.125 3.25 0 3.5 1 4 2 5 Use MODE 7

106. X Y -2 3.125 3.25 0 3.5 1 4 2 5

107. X Y -2 8 4 0 2 1 1 2 0.5 Use MODE 7

108. X Y -2 8 4 0 2 1 1 2 0.5

110. Points: (1, 0) (2, 1)

113. Shift 2units up Points: (1, 0) (3, 1) After shift: (1, 2) (3, 3)

115. X=2 X=-3

116. Shift 1unit right Points: (1, 0) (2, 1) After shift: (2, 0) (3, 1)

118. Shift 3units left and 1 unit up Points: (1, 0) (2, 1) After shift: (-2, 1) (-1, 2)

119. X=-3

120. Write an exponential function whose graph passes through the points (0, 15) and (3, 12) Now replace second point and also “a=15”

121. Write an exponential function whose graph passes through the points (0, 256) and (4, 81) Now replace second point and also “a=256”

122. Exponential growth with given rate: A house was bought for $96,000 in the year 2000. The house appreciates at a rate 7%. 1)Write an exponential equation that models the price after t years.

123. 2) Find the price in the year 2003.