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 = log log = y
8. log log

6. Write each equation in logarithmic form
= /2 = 125
12. e5 =148.4

7. Evaluate Logarithmic Expressions
13. log log 4300
15. ln log2 32
17. log5 1/ log11 1/121

8. Solve
19. logx 25 = 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