376 CHAPTER 5 Exponential and Logarithmic Functions Section You should be able to . . . Example(s) Review Exercises 5.4 1 Change exponential statements to logarithmic statements and logarithmic statements to exponential statements (p. 313) 2, 3 16, 17 2 Evaluate logarithmic expressions (p. 314) 4 15(b), (d), 20, 47(b), 49(a), 50 3 Determine the domain of a logarithmic function (p. 314) 5 18, 19, 35(a) 4 Graph logarithmic functions (p. 315) 6, 7 32–34, (d)–(f), 35(b)–(c), 47(a) 5 Solve logarithmic equations (p. 319) 8, 9 38, 47(c), 49(b) 5.5 1 Work with the properties of logarithms (p. 327) 1, 2 21, 22 2 Write a logarithmic expression as a sum or difference of logarithms (p. 329) 3–5 23–26 3 Write a logarithmic expression as a single logarithm (p. 330) 6 27–29 4 Evaluate logarithms whose base is neither 10 nor e (p. 331) 7, 8 30 5 Graph a logarithmic function whose base is neither 10 nor e (p. 332) 9 31 5.6 1 Solve logarithmic equations (p. 336) 1–3 38, 41, 44 2 Solve exponential equations (p. 338) 4–6 39, 43, 45, 46 3 Solve logarithmic and exponential equations using a graphing utility (p. 341) 7 36–46 5.7 1 Determine the future value of a lump sum of money (p. 345) 1–3 51 2 Calculate effective rates of return (p. 348) 4 51 3 Determine the present value of a lump sum of money (p. 349) 5 52 4 Determine the rate of interest or the time required to double a lump sum of money (p. 350) 6, 7 51 5.8 1 Model populations that obey the law of uninhibited growth (p. 355) 1, 2 55 2 Model populations that obey the law of uninhibited decay (p. 357) 3 53, 56 3 Use Newton’s Law of Cooling (p. 359) 4 54 4 Use logistic models (p. 360) 5, 6 57 5.9 1 Build an exponential model from data (p. 367) 1 58 2 Build a logarithmic model from data (p. 368) 2 59 3 Build a logistic model from data (p. 369) 3 60 Review Exercises In Problems 1–3, for each pair of functions f and g, find: (a) ( )( ) f g 2 (b) ( ) − g f ( ) 2 (c) ( ) f f ( ) 4 (d) ( )( ) − g g 1 1. ( ) ( ) = − = − f x x g x x 3 5; 1 2 2 2. ( ) ( ) = + = + f x x g x x 2; 2 1 2 3. ( ) ( ) = = − f x e g x x ; 3 2 x In Problems 4–6, find f g g f f f , , , and g g for each pair of functions. State the domain of each composite function. 4. ( ) ( ) = − = + f x x g x x 2 ; 3 1 5. ( ) ( ) = = + + f x x g x x x 3 ; 1 2 6. ( ) ( ) = + − = f x x x g x x 1 1 ; 1 7. (a) Verify that the function below is one-to-one. (b) Find its inverse. ( ) ( ) ( ) ( ) { } 1, 2 , 3, 5 , 5, 8 , 6, 10
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