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Chapter 4.5

Chapter 4.5. Exponential and Logarithm Functions. Exponential Equations. We solved exponential equations in earlier sections. General methods for solving these equations depend on the property below, which follows from the fact that lorarithmic functions are one-to-one. Solve 7 x = 12.

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Chapter 4.5

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  1. Chapter 4.5 Exponential and Logarithm Functions

  2. Exponential Equations We solved exponential equations in earlier sections. General methods for solving these equations depend on the property below, which follows from the fact that lorarithmic functions are one-to-one.

  3. Solve 7x = 12. Give the solution to four decimal places.

  4. Caution Be careful when evaluating a quotient like

  5. Solve 32x-1 = .4x+2 Give the solution to four decimal places.

  6. Solve 32x-1 = .4x+2 Give the solution to four decimal places.

  7. Solve the equation Give the solution to four decimal places.

  8. Solve the equation Give the solution to four decimal places.

  9. Solve the equation Give the solution to four decimal places.

  10. Solve the equation Give the solution to four decimal places.

  11. Logarithmic Equations The next examples show some ways to solve logarithmic equations.

  12. Solve

  13. Logarithmic Equations The negative solution x = -3 is not in the domain of logax in the original equation, so the only valid solution is the positive number 2, giving the solution set {2}.

  14. Solve

  15. Solve

  16. Logarithmic Equations The number is negative, so x-1 is negative. So log (x-1) is not defined and this solution is not in the domain. The solution set is

  17. Solve

  18. The strength of a habit is a function of the number of times the habit is repeated. If N is the number of repetitions and H is the strength of the habit, then, according to psychologist C. L. Hull where k Is a constant .

  19. Solve this equation for k.

  20. Solve this equation for k.

  21. Solve this equation for k.

  22. The table gives U. S. coal consumption (in quadrillions of British thermal units, or quads) for several years. The data can be modeled with the functions defined by where t is the number of years after 1900, and f(t) in quads.

  23. Approximately what amount of coal was consumed in the United States in 1993?

  24. If this trend continues, approximately when will annual consumption reach 25 quads?

  25. If this trend continues, approximately when will annual consumption reach 25 quads? Annual consumption will reach 25 quads in the year 2010.

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