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Lesson 5-6: Logarithms and Logarithmic Functions

Lesson 5-6: Logarithms and Logarithmic Functions. Advanced Math Topics. Key Concept. Logarithms with base b Read: “Log of x base b is y”. Key Concepts. Common Logarithm: log 10 can just be written log Log 100 is the same as log 10 100

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Lesson 5-6: Logarithms and Logarithmic Functions

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  1. Lesson 5-6: Logarithms and Logarithmic Functions Advanced Math Topics

  2. Key Concept • Logarithms with base b • Read: “Log of x base b is y”

  3. Key Concepts • Common Logarithm: log10 can just be written log • Log 100 is the same as log10 100 • There is a button on your calculator for log you can only use it when you are dealing with base 10! • Natural Logarithm: loge is called the natural log and is written ln • Loge1 is the same as the ln 1 • There is a button on your calculator for ln you can use this anytime you see ln in a problem!

  4. Logarithmic to Exponential Form 1. log6 216 = 3 2. log4 1 = 0 3. log3 81 = 4 4. ln e2 = 2 5. log 40 = 1.6

  5. Exponential to Logarithmic Form 6. y = log10 100 7. log2 0.25 = y 8. log5 625 9. log10 0.001

  6. Write each equation in logarithmic form 10. 29 = 512 11. 0.04-3/2 = 125 12. e5 =148.4

  7. Evaluate Logarithmic Expressions 13. log 43 14. log 4300 15. ln 0.05 16. log2 32 17. log5 1/125 18. log11 1/121

  8. Solve 19. logx 25 = 2 20. logx 9/100 = -2 20. logx = 1/2

  9. Characteristics of Logarithmic Functions • 1. Inverse of the exponential function y=bx • 2.Continous and one-to-one • 3. Domain is all positive real numbers • 4. y-axis is an asymptote • 5. Range is ARN • 6. Contains (1,0), so x-intercept is 1

  10. Helpful Hint • Since exponential and logarithmic functions are inverses if the bases are the same they “undo” each other…

  11. Logarithmic Equations • Property of Equality • If b is a positive number other than 1, then if and only if x = y.

  12. Example 4 • Solve

  13. Example 5 • Solve

  14. Example 6 • Solve

  15. Example 7 • Solve

  16. Example 8 • Solve

  17. Example 9 • Solve

  18. Example 10 • Solve

  19. Example 11 • Solve

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