College Math

College Math Study Guide

Let us solve an example using these rules of exponents. Simplify the following expression: (5 −1 6 −2 ) −3 (10 3 −3 ) 3 = 5 −1(−3) 6(−3) −2(−3) 10 1(3) 3(3) −3(3) = 5 3 −18 6 10 3 9 −9 = 125 −18−9 6−(−9) 1000 = −27 15 8 = 15 8 27 1.13 Logarithm Functions A logarithm function is the function that is written in the form of: ( ) = log , such that > 0 and ≠ 1 If = 2 , then ( ) = log 2 2 ( ) = Assuming different positive values of (it is necessary that 2 ( ) > 0) , log 2 ( ) ( , ) When we plot these values in the graph, we get the following graphical representation:

1 4 log 2 � 1 4 � = −2 −2 � 1 4 , −2� 1 2 log 2 � 1 2 � = −1 −1 � 1 2 , −1� 1 log 2 (1) = 0 0 (1,0) 2 log 2 (2) = 1 1 (2,1) 4 log 2 (4) = 2 2 (4,2)

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