5_5 - Chapter 5 Exponential and Logarithmic Functions 5.5...

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Chapter 5 694 Exponential and Logarithmic Functions 5.5 Properties of Logarithms 1. sum 2. 7 3. r log a M 4. False 5. False 6. True 7. log 3 3 71 = 71 8. log 2 2 - 13 = - 13 9. ln e - 4 =- 4 10. ln e 2 = 2 11. 2 log 2 7 = 7 12. e ln8 = 8 13. log 8 2 + log 8 4 = log 8 4 2 ( 29 = log 8 8 = 1 14. log 6 9 + log 6 4 = log 6 9 4 ( 29 = log 6 36 = log 6 6 2 = 2 15. log 6 18 - log 6 3 = log 6 18 3 = log 6 6 = 1 16. log 8 16 - log 8 2 = log 8 16 2 = log 8 8 = 1 17. log 2 6 log 6 4 = log 6 4 log 2 6 = log 6 2 2 ( 29 log 2 6 = log 6 2 ( 29 2log 2 6 = log 6 2 ( 29 log 2 6 2 = log 6 6 2 = 2 18. log 3 8 log 8 9 = log 8 9 log 3 8 = log 8 3 2 ( 29 log 3 8 = log 8 3 ( 29 2log 3 8 = log 8 3 ( 29 log 3 8 2 = log 8 8 2 = 2 19. 3 log 3 5 - log 3 4 = 3 log 3 5 4 = 5 4 20. 5 log 5 6 + log 5 7 = 5 log 5 6 7 ( 29 = 6 7 = 42
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Section 5.5 Properties of Logarithms 695 21. e log e 2 16 22. e log e 2 9 Simplify the exponent. Let a = log e 2 16, then e 2 ( 29 a = 16. e 2 a = 16 e 2 a = 4 2 e 2 a ( 29 1/2 = 4 2 ( 29 1/2 e a = 4 a = ln4 Thus, e log e 2 16 = e ln4 = 4. Simplify the exponent. Let a = log e 2 9, then e 2 ( 29 a = 9. e 2 a = 9 e 2 a = 3 2 e 2 a ( 29 1/2 = 3 2 ( 29 1/2 e a = 3 a = ln3 Thus, e log e 2 9 = e ln3 = 3. 23. ln6 = ln(3 2) = ln3 + ln2 = b + a 24. ln 2 3 = ln2 - ln3 = a - b 25. ln1.5 = ln 3 2 = ln3 - ln2 = b - a 26. ln0.5 = ln 1 2 = ln1 - ln2 = 0 - a = - a 27. ln8 = ln2 3 = 3 ln2 = 3 a 28. ln27 = ln3 3 = 3 ln3 = 3 b 29. ln 6 5 = ln6 1/5 = 1 5 ln6 = 1 5 ln 2 3 ( 29 = 1 5 ln2 + ln3 ( 29 = 1 5 a + b ( 29 30. ln 2 3 4 = ln 2 3 1/4 = 1 4 ln 2 3 = 1 4 ln2 - ln3 ( 29 = 1 4 a - b ( 29 31. log 5 25 x ( 29 = log 5 25 + log 5 x = 2 + log 5 x 32. log 3 x 9 = log 3 x - log 3 9 = log 3 x - 2 33. log 2 z 3 = 3log 2 z 34. log 7 x 5 = 5log 7 x 35. ln ex ( 29 = ln e + ln x = 1 + ln x 36. ln e x = ln e - ln x = 1 - ln x 37. ln xe x ( 29 = ln x + ln e x = ln x + x 38. ln x e x  = ln x - ln e x = ln x - x 39. log a u 2 v 3 ( 29 = log a u 2 + log a v 3 = 2log a u + 3log a v 40. log 2 a b 2  = log 2 a - log 2 b 2 = log 2 a - 2log 2 b
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Chapter 5 Exponential and Logarithmic Functions 696 41. ln x 2 1 - x ( 29 = ln x 2 + ln 1 - x = ln x 2 + ln(1 - x ) 1/2 = 2ln x + 1 2 ln(1 - x ) 42. ln x 1 + x 2 ( 29 = ln x + ln 1 + x 2 = ln x + ln(1 + x 2 ) 1/2 = ln x + 1 2 ln(1 + x 2 ) 43. log 2 x 3 x - 3 = log 2 x 3 - log 2 ( x - 3) = 3log 2 x - log 2 ( x
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This homework help was uploaded on 04/07/2008 for the course MAC 1105 taught by Professor Any during the Spring '08 term at FIU.

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5_5 - Chapter 5 Exponential and Logarithmic Functions 5.5...

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