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Warm-Up: January 31, 2012

Warm-Up: January 31, 2012. Suppose that you have $500 to invest. Which investment yields the greatest return over 6 years: 3.68% compounded semi-annually (twice a year) or 3.65% compounded continuously?. Homework Questions?. Logarithmic Functions. Section 3.2. Logarithmic Function.

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Warm-Up: January 31, 2012

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  1. Warm-Up: January 31, 2012 • Suppose that you have $500 to invest. Which investment yields the greatest return over 6 years: 3.68% compounded semi-annually (twice a year) or 3.65% compounded continuously?

  2. Homework Questions?

  3. Logarithmic Functions Section 3.2

  4. Logarithmic Function • For x>0, b>0, b≠1 • The function is the logarithmic function with base “b”

  5. Converting Forms Exponential form Logarithmic form 103 = 10003 = log101000 Exponent Base

  6. Example 1 (like HW #1-8) • Write in exponential form

  7. You-Try #1 (like HW #1-8) • Write in exponential form

  8. Example 2 (like HW #12-20) • Write in logarithmic form

  9. You-Try #2 (like HW #12-20) • Write in logarithmic form

  10. Evaluating Logarithms • To evaluate logbx, ask, “b to what power gives x?” • For log232, “2 to what power gives 32?” • log232 = 5

  11. Example 3 (like HW #21-30) • Evaluate each logarithm

  12. You-Try #3 (like HW #21-30) • Evaluate each logarithm

  13. Logarithmic Properties with 1

  14. You-Try #4

  15. Inverse Properties of Logs • For b>0 and b≠1

  16. You-Try #5 - Simplify

  17. y = x f (x) = 2x 6 5 4 3 f (x) = log2x 2 -2 -1 2 3 4 5 6 -1 -2 Graphs of f(x)=logbx

  18. Graphs of f(x)=logbx • The x-intercept is 1 • There is no y-intercept • The y-axis is a vertical asymptote • If b>1, then the function is increasing • If 0<b<1, then the function is decreasing • The graph is smooth and continuous

  19. Common Logarithm • A logarithm with base 10 is called the common logarithm. • The common logarithm is often written without the base • Use the [LOG] button on your TI-83

  20. Natural Logarithm • A logarithm with base e (the natural base) is called the natural logarithm. • The natural log is usually written with “ln” instead of “log” • Use the [LN] button on your TI-83

  21. Properties of Logarithms • General Properties • Common Logarithms • Natural Logarithms

  22. Example 11 • Simplify

  23. You-Try #11 • Simplify

  24. Assignment • Page 377 #1-37 odd, 61-79 odd, 83

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