# 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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