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Precalculus Lesson ( )

Precalculus Lesson ( ). 3.3. Check: p. 270 #4, 8, 20, 24, 34, 36, 40, 44, 46, 56. Warm-up. Answers. Objective:. Use the change of base formula, and properties of logarithms. Lesson. Quiz 3.1-3.2 [IF no time yesterday]

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Precalculus Lesson ( )

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  1. PrecalculusLesson ( ) 3.3 Check: p. 270 #4, 8, 20, 24, 34, 36, 40, 44, 46, 56

  2. Warm-up

  3. Answers

  4. Objective: Use the change of base formula, and properties of logarithms.

  5. Lesson • Quiz 3.1-3.2 [IF no time yesterday] • smartboard3.3-- students watch, then fill in example on Notes 3.3

  6. given: logb 12  1.5440 logb 10  1.4307 Properties of Logarithms For m > 0, n > 0, b > 0, and b  1: Product Property logb (mn) = logb m + logb n logb 120 = logb (12)(10) = logb 12 + logb 10 1.5440 + 1.4307 2.9747

  7. given: logb 12  1.5440 logb 10  1.4307 logb = logb m – logb n 12 = logb 10 m n Properties of Logarithms For m > 0, n > 0, b > 0, and b  1: Quotient Property logb 1.2 = logb 12 – logb 10 1.5440 – 1.4307 0.1133

  8. Review Properties of Logarithms For m > 0, n > 0, b > 0, and any real number p: Power Property logb mp = p logb m Using the power property log5 1254 5x = 125 = 4 log5 125 53 = 125 =4  3 x = 3 = 12

  9. Properties of Logarithms For b > 0 and b  1: Exponential-Logarithmic Inverse Property logb bx = x and b logbx = x for x > 0

  10. Just watch--Example Evaluate each expression. a) b)

  11. Try these--Practice (on hand-out) Evaluate each expression. 1) 7log711 – log3 81 2) log8 85 + 3log38

  12. Properties of Logarithms For b > 0 and b  1: One-to-One Property of Logarithms If logb x = logb y, then x = y

  13. Just watch--Example 2 Solve log2(2x2 + 8x – 11) = log2(2x + 9) for x. log2(2x2 + 8x – 11) = log2(2x + 9) 2x2 + 8x – 11 = 2x + 9 2x2 + 6x – 20 = 0 2(x2 + 3x – 10) = 0 2(x – 2)(x + 5) = 0 x = -5,2 Check: log2(2x2 + 8x – 11) = log2(2x + 9) log2 (–1) = log2 (-1) undefined log2 13 = log2 13 true

  14. Try these--Practice (on hand-out) Solve for x. 3) log5 (3x2 – 1) = log5 2x 4) logb (x2 – 2) + 2 logb 6 = logb 6x

  15. Assignments Classwork: If time: puzzle “joke 14” Homework(3.3) P. 241 #20, 22, 28, 32, 36, 44, 54, 58, 78, 84

  16. Closure 3.2

  17. Closure

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