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Exponential Equations & Logarithmic Functions: Solving Methods and Investment Strategies

Explore methods to solve exponential equations with one solution, find investment growth using different compounding methods. Learn about logarithmic functions, their role in science scales, and natural logarithmic functions.

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Exponential Equations & Logarithmic Functions: Solving Methods and Investment Strategies

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  1. Exponential Equations Like Bases

  2. Warm Up • The following quadratic equation has exactly one solution for x. Find the value of k. Explore more than one method…..

  3. Method One • One solution indicates that the discriminant is equal to 0:

  4. Method Two

  5. Warm Up - If $5,000 is invested at an interest rate of 5% per year, find the amount of the investment at the end of 5 years for the following compounding methods: • Annually • Monthly • Quarterly • Continuously

  6. Annually: Monthly:

  7. Quarterly: Continuously

  8. Logarithmic Functions

  9. Logarithms • Used to find unknown exponents in exponential models • Define many measurement scales in the sciences such as the pH, decibel, and Richter scales.

  10. For any positive base b, where b≠1: bx = y if and only if x = logby Exponential Form Logarithmic Form

  11. Write in logarithmic form.

  12. Write in logarithmic form.

  13. Write in logarithmic form.

  14. Natural log

  15. The Natural Logarithmic Function • The natural logarithmic function is the inverse of the natural exponential function

  16. Write in logarithmic form.

  17. Write in exponential form.

  18. Write in exponential form.

  19. Write in exponential form.

  20. Write in exponential form.

  21. Find the value of x.

  22. Find the value of x.

  23. Find the value of x.

  24. Find the value of x.

  25. Find the value of x.

  26. Find the value of x.

  27. Find the value of x.

  28. Find the value of x.

  29. Find the value of x.

  30. Find the value of x.

  31. Solve

  32. Find to the nearest thousandth – using the calculator.

  33. Find to the nearest thousandth – using the calculator.

  34. Find to the nearest thousandth – using the calculator.

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