4_3 - Section 4.3: Logarithmic Functions Instructor: Ms....

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Section 4.3: Logarithmic Functions Instructor: Ms. Hoa Nguyen (nguyen@scs.fsu.edu) 1 Logarithmic Functions An exponential function y = f ( x ) = a x with a > 0, a 6 = 1 is one-to-one . Then its inverse function f - 1 is the logarithmic function x = f - 1 ( y ) = log a y . In other words, L = R p ⇐⇒ p = log R L . Consequently, we have: log a 1 = 0 because a 0 = 1. log a a = 1 because a 1 = a . Example 1 : Example 2 : 1
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f - 1 ( y ) = log a y for all y in the range of f ( x ) = a x . The same as saying: f - 1 ( x ) = log a x for all x in the range of f ( x ) = a x . y = log a x is read as “ y is the logarithm to the base a of x ”. Since the exponential function and the logarithm function are inverses, denote f ( x ) = log a x and f - 1 ( x ) = a x . From Section 4 . 2, we know that: The domain of the exponential function f - 1 is the set of ALL real numbers. The range of the exponential function f - 1 is the set of positive real numbers. Then, what can we say about the domain and range of
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4_3 - Section 4.3: Logarithmic Functions Instructor: Ms....

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