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College Algebra Chapter 4 Exponential and Logarithmic Functions

College Algebra Chapter 4 Exponential and Logarithmic Functions. Section 4.5 Exponential and Logarithmic Equations and Applications. 1. Solve Exponential Equations 2 . Solve Logarithmic Equations 3. Use Exponential and Logarithmic Equations in Applications. Solve Exponential Equations.

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College Algebra Chapter 4 Exponential and Logarithmic Functions

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  1. College AlgebraChapter 4Exponential and Logarithmic Functions Section 4.5 Exponential and Logarithmic Equations and Applications

  2. 1. Solve Exponential Equations 2. Solve Logarithmic Equations 3. Use Exponential and Logarithmic Equations in Applications

  3. Solve Exponential Equations Some exponential equations can be solved using the equivalence property of exponential expressions: If b, x, and y are real numbers with b > 0 and b ≠ 1, then

  4. Example 1: Solve

  5. Example 2: Solve

  6. Example 3: Solve

  7. Solve Exponential Equations Most exponential equations cannot be rewritten to have matching bases. To solve these equations, isolate the exponential expression, take a logarithm of both sides, and then apply the power property of logarithms.

  8. Example 4: Solve

  9. Example 5: Solve

  10. Example 6: Solve

  11. Example 7: Solve

  12. Example 8: Solve (quadratic in form)

  13. 1. Solve Exponential Equations 2. Solve Logarithmic Equations 3. Use Exponential and Logarithmic Equations in Applications

  14. Solve Logarithmic Equations Note the difference between these two equations: In the first equation, all terms have a logarithm. The second equation is a mix of logarithmic and constant terms. These two equations require different styles of solution.

  15. Solve Logarithmic Equations For solving equations of the first type, we will use the equivalence property of logarithmic expressions. If b, x, and y are real numbers with b > 0 and b ≠ 1, then

  16. Example 9: Solve

  17. Example 10: Solve

  18. Example 11: Solve

  19. Example 12: Solve

  20. Example 13: Solve

  21. Solve Logarithmic Equations To solve equations that are a mix of logarithms and constants, collect all logarithms together, then rewrite the equation in exponential form. (k is a constant)

  22. Example 14: Solve

  23. Example 15: Solve

  24. Example 16: Solve

  25. Example 17: Solve

  26. 1. Solve Exponential Equations 2. Solve Logarithmic Equations 3. Use Exponential and Logarithmic Equations in Applications

  27. Example 18: If $20,000 is invested in an account earning 2.5% interest compounded continuously, determine how long it will take the money to grow to $45,000. Round to the nearest year. Use the model .

  28. Example 19: The following formula relates the energy E (in joules) released by an earthquake of magnitude M. (M > 5) What is the energy released by a magnitude 6 and a magnitude 7 earthquake?

  29. Example 19 continued: As a comparison, a 1 megaton nuclear weapon would have an energy release of joules and the eruption of the volcano Krakatoa in 1883 produced an energy release of joules.

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