5_6 - Chapter 5 Exponential and Logarithmic Functions 5.6 1...

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Chapter 5 705 Exponential and Logarithmic Functions 5.6 Logarithmic and Exponential Equations 1. log 4 ( x + 2) = log 4 8 x + 2 = 8 x = 6 The solution set is 6 { } . 2. log 5 (2 x + 3) = log 5 3 2 x + 3 = 3 2 x = 0 x = 0 The solution set is 0 { } . 3. 1 2 log 3 x = 2log 3 2 log 3 x 1/2 = log 3 2 2 x 1/2 = 4 x = 16 The solution set is 16 { } . 4. - 2log 4 x = log 4 9 log 4 x - 2 = log 4 9 x - 2 = 9 1 x 2 = 9 x 2 = 1 9 x = ± 1 3 Since log 4 - 1 3 is undefined, the solution set is 1 3 . 5. 2log 5 x = 3log 5 4 log 5 x 2 = log 5 4 3 x 2 = 64 x = ± 8 Since log 5 - 8 ( 29 is undefined, the solution set is 8 { } . 6. 3log 2 x = - log 2 27 log 2 x 3 = log 2 27 - 1 x 3 = 27 - 1 x 3 = 1 27 x = 1 3 The solution set is 1 3 .
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Chapter 5 Exponential and Logarithmic Functions 706 7. 3log 2 ( x - 1) + log 2 4 = 5 log 2 ( x - 1) 3 + log 2 4 = 5 log 2 4( x - 1) 3 ( 29 = 5 4( x - 1) 3 = 2 5 ( x - 1) 3 = 32 4 ( x - 1) 3 = 8 x - 1 = 2 x = 3 The solution set is 3 { } . 8. 2log 3 ( x + 4) - log 3 9 = 2 log 3 ( x + 4) 2 - log 3 3 2 = 2 log 3 ( x + 4) 2 - 2 = 2 log 3 ( x + 4) 2 = 4 ( x + 4) 2 = 3 4 ( x + 4) 2 = 81 x + 4 = ± 9 x = - 4 ± 9 x = 5 or x = - 13 Since log 3 - 13 + 4 ( 29 = log 3 - 9 ( 29 is undefined, the solution set is 5 { } . 9. log x + log( x + 15) = 2 log x ( x + 15) ( 29 = 2 x ( x + 15) = 10 2 x 2 + 15 x - 100 = 0 ( x + 20)( x - 5) = 0 x = - 20 or x = 5 Since log - 20 ( 29 is undefined, the solution set is 5 { } . 10. log 4 x + log 4 ( x - 3) = 1 log 4 x ( x - 3) ( 29 = 1 x ( x - 3) = 4 1 x 2 - 3 x - 4 = 0 ( x + 1)( x - 4) = 0 x = - 1 or x = 4 Since log 4 - 1 ( 29 is undefined, the solution set is 4 { } . 11. ln x + ln( x + 2) = 4 ln x ( x + 2) ( 29 = 4 x ( x + 2) = e 4 x 2 + 2 x - e 4 = 0 x = - 2 ± 2 2 - 4(1)( - e 4 ) 2(1) = - 2 ± 4 + 4 e 4 2 = - 2 ± 2 1 + e 4 2 = - 1 ± 1 + e 4 x = - 1 - 1 + e 4 or x = - 1 + 1 + e 4 ≈ - 8.456 6.456 Since ln - 8.456 ( 29 is undefined, the solution set is - 1 + 1 + e 4 6.456 { } .
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Section 5.6 Logarithmic and Exponential Equations 707 12. ln( x + 1) - ln x = 2 ln x + 1 x = 2 x + 1 x = e 2 x + 1 = e 2 x e 2 x - x = 1 x e 2 - 1 ( 29 = 1 x = 1 e 2 - 1 0.156 The solution set is 1 e 2 - 1 0.156 . 13. 2 2 x + 2 x - 12 = 0 2 x ( 29 2 + 2 x - 12 = 0 2 x - 3 ( 29 2 x + 4 ( 29 = 0 2 x - 3 = 0 or 2 x + 4 = 0 2 x = 3 or 2 x = - 4 x = log 2 3 No solution = log3 log2 1.585 The solution set is log 2 3 1.585 { } . 14. 3 2 x + 3 x - 2 = 0 3 x ( 29 2 + 3 x - 2 = 0 3 x - 1 ( 29 3 x + 2 ( 29 = 0 3 x - 1 = 0 or 3 x + 2 = 0 3 x = 1 or 3 x = - 2 x = 0 No solution The solution set is 0 { } .
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Chapter 5 Exponential and Logarithmic Functions 708 15. 3 2 x + 3 x + 1 - 4 = 0 3 x ( 29 2 + 3 3 x - 4 = 0 3 x - 1 ( 29 3 x + 4 ( 29 = 0 3 x - 1 = 0 or 3 x + 4 = 0 3 x = 1 or 3 x = - 4 x = 0 No solution The solution set is 0 { } . 16.
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This note 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_6 - Chapter 5 Exponential and Logarithmic Functions 5.6 1...

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