Chapter 8

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Reflecting A. Solutions A and B used the exponential form of the model, but different strategies. Which one of these strategies will only work for some equations? Explain why. B. Solution C used the logarithmic form of the model. Is there any advantage of rewriting the model in this form? Explain. C. If you had to solve the equation 3 t11 5 1000, which strategy would you use? Explain your reasons. 8.3 APPLY the Math EXAMPLE 2 Using reasoning to evaluate logarithmic expressions Use the definition of a logarithm to determine the value of each expression. a) log 4 64 c) log 2 (24) b) log 3 a 1 27 b d) log 5 " 3 25 Solution a) log 4 64 5 x Determine the exponent to which 4 must be raised to get 64. 4 x 5 64 4 x 5 4 3 x 5 3 Rewrite the equation in exponential form. Rewrite 64 as a power of 4. The exponent is 3. b) log 3 a 1 27 b 5 x Determine the exponent to which 3 must be raised to get 1 27 . 3 x 5 1 27 Rewrite the equation in exponential form. 3 x 5 3 23 1 Since can be replaced 27 5 1 3 3, 1 27 with 3 23 . x 523 The exponent is 23. NEL <strong>Chapter</strong> 8 461
c) log 2 (24) 5 x Determine the exponent to which 2 must be raised to get 24. 2 x 524 Rewrite the equation in exponential form. There is no solution. 8 4 y y = 2 x 0 –4 –2 2 4 –4 x Since 2 is a positive number, there will never be a negative result when 2 is raised to an exponent. The domain of any logarithmic function is x . 0. Recall that the range of y 5 2 x is 5 yPR 0 y . 06. d) log 5 " 3 25 5 x Determine the exponent to which 5 must be raised to get " 3 25. 5 x 5 " 3 25 5 x 5 " 3 5 2 5 x 5 5 2 3 x 5 2 3 Rewrite the radical using the equivalent fractional exponent. The exponent is . 2 3 EXAMPLE 3 Selecting a strategy to estimate the logarithm of a number Determine the approximate value of log 5 47. Solution A: Using graphing technology log 5 47 5 x 5 x 5 47 Determine the exponent to which 5 must be raised to get 47. Rewrite the equation in exponential form. 462 8.3 Evaluating Logarithms NEL
Page 1 and 2: 444 NEL
Page 3 and 4: 8 Getting Started Study Aid • For
Page 5 and 6: 8.1 Exploring the Logarithmic Funct
Page 7 and 8: In Summary Key Ideas • The invers
Page 9 and 10: 8.2 Transformations of Logarithmic
Page 11 and 12: Reflecting L. Describe the domain a
Page 13 and 14: EXAMPLE 2 Connecting a geometric de
Page 15 and 16: PRACTISING 4. Let f (x) 5 log 10 x.
Page 17: Solution B: Using a graphing calcul
Page 21 and 22: EXAMPLE 4 Selecting a strategy to e
Page 23 and 24: CHECK Your Understanding 1. Express
Page 25 and 26: 17. The doubling function y 5 y 0 2
Page 27 and 28: log a (mn) 5 x 1 y m 5 a x so log a
Page 29 and 30: APPLY the Math EXAMPLE 4 Selecting
Page 31 and 32: EXAMPLE 6 Selecting strategies to s
Page 33 and 34: 9. Write each expression as a singl
Page 35 and 36: Study • See Lesson 8.2, Examples
Page 37 and 38: 8.5 Solving Exponential Equations G
Page 39 and 40: Solution C: Solving the equation gr
Page 41 and 42: EXAMPLE 4 Solve 2 x11 5 3 x21 to th
Page 43 and 44: 8. Solve for x. a) 4 x11 1 4 x 5 16
Page 45 and 46: Reflecting A. What strategies for s
Page 47 and 48: x 2 2 9 5 2 4 x 2 2 9 5 16 x 2 5 25
Page 49 and 50: 9. The loudness, L, of a sound in d
Page 51 and 52: APPLY the Math EXAMPLE 1 Solving a
Page 53 and 54: EXAMPLE 2 Representing exponential
Page 55 and 56: Solution Sound Loudness (dB) soft w
Page 57 and 58: 6. Calculate to two decimal places
Page 59 and 60: 8.8 Rates of Change in Exponential
Page 61 and 62: EXAMPLE 2 Selecting a strategy for
Page 63 and 64: Solution -2 Tangents to y = 10 x y
Page 65 and 66: y 8 y = log x - 1 6 2 d 4 2 y = - 1
Page 67 and 68: PRACTICE Questions Lesson 8.1 1. De
Page 69 and 70:
8 Chapter Self-Test 1. Write the eq
Page 71 and 72:
2(sec 2 x 2 tan 2 x) 9. 5 sin 2x se
Page 73 and 74:
d) D 5 5xPR 0 x . 06, R 5 5 yPR6 e)
Page 75 and 76:
17. log b x!x 5 log b x 1 log b !x
Page 77:
value of x. Determine the average r
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Chapter 8

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