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3.2 Logarithmic Functions and Their Graphs

3.2 Logarithmic Functions and Their Graphs. Definition of Logarithmic Function. 2 3 = 8. Ex. 3 = log 2 8. Ex. log 2 8. = x. 2 x = 8. x = 3. Properties of Logarithms and Natural Logarithms. log a 1 = 0 log a a = 1 log a a x = x. ln 1 = 0 ln e = 1 ln e x = x. Ex.

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3.2 Logarithmic Functions and Their Graphs

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  1. 3.2 Logarithmic Functions and Their Graphs Definition of Logarithmic Function 23 = 8 Ex. 3 = log2 8

  2. Ex. log28 = x 2x = 8 x = 3 Properties of Logarithms and Natural Logarithms • loga 1 = 0 • loga a = 1 • loga ax = x • ln 1 = 0 • ln e = 1 • ln ex = x

  3. Ex. Use the definition of logarithm to write in logarithmic form. Ex. 4x = 16 log4 16 = x e2 = x ln x = 2

  4. Graph and find the domain of the following functions. y = ln x x y -2 -1 0 1 2 3 4 .5 cannot take the ln of a (-) number or 0 0 ln 2 = .693 ln 3 = 1.098 ln 4 = 1.386 D: x > 0 ln .5 = -.693

  5. Graph y = 2x y = x x y -2 -1 0 1 2 2-2 = 2-1 = 1 2 4 The graph of y = log2 x is the inverse of y = 2x.

  6. The domain of y = b +/- loga (bx + c), a > 1 consists of all x such that bx + c > 0, and the V.A. occurs when bx + c = 0. The x-intercept occurs when bx + c = 1. Ex. Find all of the above for y = log3 (x – 2). Sketch. D: x – 2 > 0 D: x > 2 V.A. @ x = 2 x-int. x – 2 = 1 x = 3 (3,0)

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