ss_4_3

# ss_4_3 - Section 4.3 Logarithmic Functions Denition. y =...

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Section 4.3 Logarithmic Functions Deﬁnition. y =log 10 x iﬀ x =10 y . The number 10 is called the base of the logarithm. Notation. It is customary to write y x for y 10 x . The number log 10 x is called the common logarithm of x . Example. Since 10 2 = 100, log 10 100 = 2. The graphs of y x and y x are shown below. –1 0 1 2 3 4 5 –2 –1 1 2 y x –2 –1 0 1 2 12345 y 10 x Note: The functions y 10 x and y x are inverse functions, i.e., if f ( x )=log 10 x ,th en f - 1 ( x )=10 x . Since the exponential function and the log function are inverses, we have the following. 10 log x = x log 10 x = x The graphs of y x and y x are shown together below. –4 –2 0 2 4 –4 –2 2 4 y x and y x The function f ( x a x can be deﬁned for any number a> 0, a 6 = 1. The deﬁnition for any a is analogous to the deﬁnition for a = 10. Deﬁnition. y a x iﬀ x = a y , 0, a 6 =1. The functions f ( x a x and f - 1 ( x )= a x are inverse functions for any 0, a 6 =1 . Thus ,we have the following.

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## This note was uploaded on 12/11/2011 for the course MAC 1140 taught by Professor Kutter during the Fall '11 term at FSU.

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ss_4_3 - Section 4.3 Logarithmic Functions Denition. y =...

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