1. Logarithmic Scales
Lesson 4.4A

2. Graphing Difficult Data
Some data can be easily considered on a linear scale: 
Weights of a team of football players
Heights of a team of volleyball players
GPA's of a class of students

3. Graphing Difficult Data
Other things are more difficult to represent on a linear graph due to the vast range of values 
There are data of several orders of magnitude
Examples
distance to the moon, to planets
light brightness
loudness of a sound

4. How to Graph These Numbers?
Consider the vast range of the numbers
Distance from the Sun
Object
Distance (million km)
Mercury 58
Venus
108
Earth
149
Mars
228
Jupiter
778
Saturn
1426
Uranus
2869
Neptune
4495
Pluto
5900
Proxima Centauri
4.1E+07
Andromeda Galaxy
2.4E+13

5. How to Graph These Numbers?
What's wrong with this picture?

6. How to Graph These Numbers?
What's wrong with this picture?
We need a way to set a scale that fits all the data

7. How to Graph These Numbers?
The solution: Set the scale to be the exponent of the distance
This is called a logarithmic scale

8. Using Exponents to Indicate Distance
Consider the following problem: 
Given a number y ...   what value of x exists such that  x y  
0 .. 1
1 .. 2

9. Using Exponents to Indicate Distance
Note the value we need to represent for Mercury's distance from the sun at 58 million kilometers,
n, exponent
1.5
1.55
1.6
1.65
1.70
1.75
1.80
1.85
1.90
1.95
2.00
10n
31.62
35.48
39.81
44.67
50.12
56.23
63.10
70.79
79.43
893.1
100
Somewhere between these two
For Mercury at 58 million km  58 =

10. Assignment
Lesson 4.4A
Page 181
Exercises
1 – 5, 9, 11, 13, 15