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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 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!

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

Exponential to Logarithmic Form

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

Write each equation in logarithmic form

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

Evaluate Logarithmic Expressions

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

Solve

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

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

Helpful Hint

- Since exponential and logarithmic functions are

inverses if the bases are the same they undo

each other

Logarithmic Equations

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

y.

Example 4

- Solve

Example 5

- Solve

Example 6

- Solve

Example 7

- Solve

Example 8

- Solve

Example 9

- Solve

Example 10

- Solve

Example 11

- Solve