Economics 2301 Lecture 8 Logarithms. Base 2 and Base 10 Logarithms Base 2 LogarithmsBase 10 Logarithms Log 2 (0.25)=-2since 2 -2 =1/4Log 10 (0.01)=-2since.

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Presentation transcript:

Economics 2301 Lecture 8 Logarithms

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

Figure 3.4 Base 2 and Base 10 Logarithms

Rules of logarithmic transformations

Relationship between logarithms with different bases

Key Transformation

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

Properties of natural logarithms

Rule of 70

Graphing Grow Data

Graphing Log of income

The log Transformation