1. 3.2 Logarithmic Functions and Their Graphs Definition of Logarithmic Function Ex. 3 = log 2 8 2 3 = 8

2. Ex.log 2 8 = x 2 x = 8 x = 3 Properties of Logarithms and Natural Logarithms 1.log a 1 = 0 2.log a a = 1 3.log a a x = x 1.ln 1 = 0 2.ln e = 1 3.ln e x = x

3. Ex. Use the definition of logarithm to write in logarithmic form. Ex. 4 x = 16log 4 16 = x e 2 = xln x = 2

4. Graph and find the domain of the following functions. y = ln x x y -2 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 ln.5 = -.693 D: x > 0

5. Graph y = 2 x x y -2 0 1 2 2 -2 = 2 -1 = 124124 The graph of y = log 2 x is the inverse of y = 2 x. y = x

6. The domain of y = b +/- log a (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 = log 3 (x – 2). Sketch. D: x – 2 > 0 D: x > 2 V.A. @ x = 2 x-int. x – 2 = 1 x = 3 (3,0)