1. Economics 2301 Lecture 8 Logarithms

2. Base 2 and Base 10 Logarithms Base 2 LogarithmsBase 10 Logarithms Log 2 (0.25)=-2since 2 -2 =1/4Log 10 (0.01)=-2since 10 -2 =1/100 Log 2 (0.5)=-1since 2 -1 =1/2Log 10 (0.1)=-1since 10 -1 =1/10 Log 2 (1)=0since 2 0 =1Log 10 (1)=0since 10 0 =1 Log 2 (2)=1since 2 1 =2Log 10 (10)=1since 10 1 =10 Log 2 (4)=2since 2 2 =4Log 10 (100)=2since 10 2 =100 Log 2 (8)=3since 2 3 =8Log 10 (1000)=3since 10 3 =1000

3. Figure 3.4 Base 2 and Base 10 Logarithms

4. Rules of logarithmic transformations

5. Relationship between logarithms with different bases

6. Key Transformation

7. Natural Logarithms A natural logarithm has as it base the exponential, e. We write natural logarithms of x as log e (x) or ln(x). Natural logarithms have many applications in economics

8. Properties of natural logarithms

9. Rule of 70

10. Graphing Grow Data

11. Graphing Log of income

12. The log Transformation