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Stitz-Zeager_College_Algebra_e-book

# Logx loge y f x lnx and y g x 4 which

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Unformatted text preview: as shown below. The y -intercept (0, 1) on the graph of f corresponds to an x-intercept of (1, 0) on the graph of f −1 . The horizontal asymptotes y = 0 on the graphs of the exponential functions become vertical asymptotes x = 0 on the log graphs. 6.1 Introduction to Exponential and Logarithmic Functions y = bx , b > 1 y = logb (x), b > 1 335 y = bx , 0 < b < 1 y = logb (x), 0 < b < 1 On a procedural level, logs undo the exponentials. Consider the function f (x) = 2x . When we evaluate f (3) = 23 = 8, the input 3 becomes the exponent on the base 2 to produce the real number 8. The function f −1 (x) = log2 (x) then takes the number 8 as its input and returns the exponent 3 as its output. In symbols, log2 (8) = 3. More generally, log2 (x) is the exponent you put on 2 to get x. Thus, log2 (16) = 4, because 24 = 16. The following theorem summarizes the basic properties of logarithmic functions, all of which come from the fact that they are inverses of exponential functions. Theorem 6.2. Properties of Logarithmic Functions: Suppose f (x) = logb...
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