Lesson 5-6: Logarithms and Logarithmic Functions - PowerPoint PPT Presentation

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Lesson 5-6: Logarithms and Logarithmic Functions

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Title: Lesson 9-2: Logarithms and Logarithmic Functions Author: Elementary/Secondary Schools Last modified by: Elementary/Secondary Schools Created Date – PowerPoint PPT presentation

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Title: Lesson 5-6: Logarithms and Logarithmic Functions


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 ybx
  • 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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