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Warm-Up: February 1, 2013

Warm-Up: February 1, 2013. The population of India was 952,108,100 in 1996 and was growing at a rate of 1.3% per year. Write the expression that would predict the population in 2000. Write the expression that would predict the population in 2010. Homework Questions?. Logarithmic Functions.

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Warm-Up: February 1, 2013

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  1. Warm-Up: February 1, 2013 • The population of India was 952,108,100 in 1996 and was growing at a rate of 1.3% per year. • Write the expression that would predict the population in 2000. • Write the expression that would predict the population in 2010

  2. Homework Questions?

  3. Logarithmic Functions Section 6.3 Part 1

  4. Essential Questions • How can we convert between logarithmic and exponential forms?

  5. One-to-One Property of Exponents

  6. Logarithm • The logarithm of a number to a certain base is the exponent to which the base must be raised to equal the number.

  7. Example 1 • Evaluate each of the following logarithms: • A) log525 • B) log28 • C) log381

  8. You-Try #1 • Evaluate each of the following logarithms

  9. Use of Logarithms (don’t copy) • pH scale in chemistry • Decibels – noise levels • Richter scale – earthquake strength • Apparent magnitude (brightness) of a star • Musical intervals – semitones

  10. Converting Forms Exponential form Logarithmic form 103 = 10003 = log101000 Exponent Base Move the base to the other side of the equation

  11. Converting Forms • You can take the log (with same base) of both sides • Or you can make both sides exponents with the same base. • Logs and exponents of the same base “cancel”

  12. Example 2 • Convert to Logarithmic form

  13. You-Try #2 • Convert to Logarithmic form

  14. Example 3 • Convert to Exponential Form

  15. You-Try #3 • Convert to Exponential Form

  16. Evaluating Logarithms • To evaluate a logbx, ask yourself, “b to what exponent gives me x?”

  17. Example 4: Solve • Solve v=log100.001

  18. You-Try #4: Solve • Solve v=log41

  19. Assignment • Page 374 #12-35, 56-67

  20. Warm-Up: February 4, 2013 • Evaluate the following logarithms

  21. Homework Questions?

  22. Logarithmic Functions Section 6.3 Part 2

  23. Essential Question • How can we solve logarithmic equations?

  24. Solving for y • Evaluate the logarithm • We did this last class

  25. Solving for b • Convert to exponential form • Use a radical or fractional exponent to isolate b • Remember b>0

  26. Example 5 – Solve for b

  27. You-Try #5 – Solve for b

  28. Solving for x • Convert to exponential form • Evaluate the exponential

  29. Example 6 – Solve for x

  30. You-Try #6 – Solve for x

  31. Assignment • Page 375 #68-85

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