Lesson 5-6: Logarithms and Logarithmic Functions

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Lesson 5-6 Logarithms and Logarithmic Functions

• Advanced Math Topics

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Key Concept

• Logarithms with base b
• Read Log of x base b is y

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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!

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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

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Exponential to Logarithmic Form

• 6. y log10 100 7. log2 0.25 y
• 8. log5 625 9. log10 0.001

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Write each equation in logarithmic form

• 10. 29 512 11. 0.04-3/2 125
• 12. e5 148.4

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Evaluate Logarithmic Expressions

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

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Solve

• 19. logx 25 2 20. logx 9/100 -2
• 20. logx 1/2

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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

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Helpful Hint

• Since exponential and logarithmic functions are
  inverses if the bases are the same they undo
  each other

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Logarithmic Equations

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

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Example 4

• Solve

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Example 5

• Solve

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Example 6

• Solve

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Example 7

• Solve

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Example 8

• Solve

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Example 9

• Solve

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Example 10

• Solve

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Example 11

• Solve