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SalasSV_07_05_ex - 412 ± CHAPTER 7 THE TRANSCENDENTAL...

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Unformatted text preview: 412 ± CHAPTER 7 THE TRANSCENDENTAL FUNCTIONS EXERCISES 7.5 Evaluate. 1. log 2 64. 2. log 2 1 64 . 3. log 64 1 2 . 4. log 10 0. 01. 5. log 5 1. 6. log 5 0. 2. 7. log 5 125. 8. log 2 4 3 . Show that the given identity holds. 9. log p xy = log p x + log p y . 10. log p 1 x = − log p x . 11. log p x y = y log p x . 12. log p x y = log p x − log p y . Find the numbers x , if any, which satisfy the given equation. 13. 10 x = e x . 14. log 5 x = 0. 04. 15. log x 10 = log 4 100. 16. log x 2 = log 3 x . 17. Estimate ln a given that e t 1 < a < e t 2 . 18. Estimate e b given that ln x 1 < b < ln x 2 . Differentiate the function. 19. f ( x ) = 3 2 x . 20. g ( x ) = 4 3 x 2 . 21. f ( x ) = 2 5 x 3 ln x . 22. F ( x ) = 5 − 2 x 2 + x . 23. g ( x ) = ± log 3 x . 24. h ( x ) = 7 sin x 2 . 25. f ( x ) = tan(log 5 x ). 26. g ( x ) = log 10 x x 2 . 27. F ( x ) = cos(2 x + 2 − x ). 28. h ( x ) = a − x cos bx ....
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