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# 832 Chapter 13 Exponential and Logarithmic Functions IMPORTANT FACTS AND CONCEPTS EXAMPLES Section 13.6 Properties for Solving Exponential and...

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832 Chapter 13 Exponential and Logarithmic Functions IMPORTANT FACTS AND CONCEPTS EXAMPLES Section 13.6 Properties for Solving Exponential and Logarithmic Equations a) If then b) If then c) If then d) If then Properties 6a–6d x = y 1 x 7 0, y 7 0 2 . log b x = log b y , log b x = log b y 1 x 7 0, y 7 0 2 . x = y , x = y . a x = a y , a x = a y . x = y , a) If then b) If then c) If then d) If then x = 2. log x = log 2, log x = log 2. x = 2, x = 5. 3 x = 3 5 , 3 x = 3 5 . x = 5, Section 13.7 The natural exponential function is where Natural logarithms are logarithms to the base e . Natural loga- rithms are indicated by the notation ln. For if then The natural logarithmic function is where the base To approximate natural exponential and natural logarithmic values, use a scientific or graphing calculator. The natural exponential function, and the natural logarithmic function, , are inverses of each other. g 1 x 2 = ln x f 1 x 2 = e x , e L 2.7183. g 1 x 2 = ln x e y = x . y = ln x , x 7 0, log e x = ln x e L 2.7183. f 1 x 2 = e x Graph and on the same set of axes. If then x = e - 2.09 = 0.1237. ln x =- 2.09, ln 5.83 L 1.7630 ± 4 ± 3 ± 2 ± 1 4 3 2 1 4 3 2 1 ± 4 ± 3 ± 2 ± 1 y ² x f ( x ) ² e x g ( x ) ² ln x x y g 1 x 2 = ln x f 1 x 2 = e x Change of Base Formula For any logarithm bases a and b , and positive number x , log a x = log b x log b a log 5 98 = log 98 log 5 L 2.8488 Properties for Natural Logarithms Product rule Quotient rule Power rule 1 x 7 0 2 ln x n = n ln x 1 x 7 0 and y 7 0 2 ln x y = ln x - ln y 1 x 7 0 and y 7 0 2 ln xy = ln x + ln y ±ln± m 5 = 5 ln m ±ln± x + 1 x + 8 = ln 1 x + 1 2 - ln 1 x + 8 2 ±ln±7 # 30 = ln 7 + ln 30 Additional Properties for Natural Logarithms and Natural Exponential Expressions Property 7 Property 8 e ln x = x , x 7 0 ln e x = x e ln 2 = 2 ±ln± e 19 = 19 Chapter 13 Review Exercises [13.1] Given and find the following. 1. 2. 3. 4. Given and find the following. 5. 6. 1 g ± f 21 x 2 1 f ± g 21 x 2 g 1 x 2 = 1 x - 3 , x Ú 3, f 1 x 2 = 6 x + 7 1 g ± f 21 - 3 2 1 g ± f 21 x 2 1 f ± g 21 3 2 1 f ± g 21 x 2 g 1 x 2 = 2 x - 5, f 1 x 2 = x 2 - 3 x + 4 05/05/2016 - RS0000000000000000000000176133 - Elementary & Intermediate Algebra for College Students, Media Update
Determine whether each function is a one-to-one function. 7. 8. 9. 10. 11. 12. In Exercises 13 and 14, for each function, find the domain and range of both and 13. 14. In Exercises 15 and 16, find and graph and on the same axes. f - 1 1 x 2 f 1 x 2 f - 1 1 x 2 x y 4 { 1 5, 3 2 , 1 6, 2 2 , 1 - 4, - 3 2 , 1 - 1, 8 2 } f - 1 1 x 2 . f 1 x 2 y = x 2 - 9 y = 1 x + 8 , x Ú- 8 e1 0, - 2 2 , 1 6, 1 2 , 1 3, - 2 2 , a 1 2 , 4 bf { 1 6, 2 2 , 1 4, 0 2 , 1 - 5, 7 2 , 1 3, 8 2 } x y x y 15. 16. 17. Yards to Feet The function converts yards, x , into inches. Find the inverse function that converts inches into yards. In the inverse function, what do x and represent? 18. Gallons to Quarts The function converts gallons, x , into quarts. Find the inverse function that converts quarts into gallons. In the inverse function, what do x and represent? [13.2] Graph the following functions. 19. 20. y = a 1 2 b x y = 2 x f - 1 1 x 2 f 1 x 2 = 4 x f - 1 1 x 2 f 1 x 2 = 36 x y = f 1 x 2 = 1 3 x - 1 y = f 1 x 2 = 4 x - 2 21. Compound Interest Jim Marino invested \$1500 in a savings account that earns 4% interest compounded quarterly. Use the compound interest formula to deter- mine the amount in Jim’s account after 5 years. A = p a 1 + r n b nt [13.3] Write each equation in logarithmic form. 22. 23. 24. Write each equation in exponential form. 25. 26. 27. Write each equation in exponential form and find the missing value. 28. 29. 30. Graph the following functions. 31. 32. y = log 1 > 2 x y = log 3 x - 3 = log 1 > 5 x 4 = log a 81 3 = log 4 x log 6 1 36 =- 2 log 1 > 4 1 16 = 2 log 2 32 = 5 5 - 3 = 1 125 81 1 > 4 = 3 8 2 = 64 Chapter 13 Review Exercises 833 © Thinkstock 05/05/2016 - RS0000000000000000000000176133 - Elementary & Intermediate Algebra for College Students, Media Update
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Chapter 13 review exercise
21.
Compound Interest Jim Marino invested \$1500 in a savings account that earns 4% interest compounded
quarterly. Use the compound interest formula to determine the...

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