1. 6.3 Logarithms and Logarithmic Functions

2. Logarithm (Any Base)

3. Rewriting Logarithmic equations

4. Rewriting Exponential equations

5. Evaluating Logarithmic expressions

6. Common Logarithm (Base 10)
Remember?
Logarithm (Any Base)
Common Logarithm (Base 10)
Natural Log (Base e)

7. Evaluating Common and Natural Logarithms
Use calculator:

8. Inverse Property 1) 2)
So, exponential and log functions undo each other

9. Examples
Simplify
Simplify
= 0
Simplify
Simplify
= 2

10. Examples
Simplify
Simplify
= 5
Simplify
Simplify
= 61

11. Examples

12. Finding inverse functions

13. Parent graphs for log functions
y = x 1
y = x

14. Graph of Natural Log Graph of Common Log y = x y = 10x y = x y = log x
y = ex
y = ln x
y = x
y = log x
y = 10x
y = x 1
Domain:
x > 0
Range:
All Real Numbers
X-intercept:
(1, 0)
Y-intercept:
Does Not Exist
Function is Increasing
y-axis is vertical asymptote