3.2 Logarithmic Function and their Graphs How Exponential and Logarithm equations can be written in different forms

Definition of Logarithmic Functions Logarithmic functions are the inverses of the exponential functions. For x > 0 and 0 < a and a ≠ 1 y =loga x iff x = ay log3 81 = 4 iff 34 = 81 Logb K = E iff bE = K

Properties of Log Loga 1 = 0 since a0 = 1 where a ≠ 0 Loga a = 1 ↔ a1 = a Loga ax = x ↔ a logax = x Loga x = Loga y ↔ x = y

Graph of the Logarithmic function f(x) = logb x

Will all the bases go through (1,0)?

Natural Log means base e Log e x means Ln x Properties stay the same Ln 1 = 0 ↔ e0 = 1 Ln e = 1 ↔ e1 = e Ln ex = x ↔ e ln x = x Ln x = Ln y ↔ x = y

Graphing a Logarithm function f(x) = log 5 x change is to y = log 5 x it would be moved around as 5y = x Fill in y and make a chart. x y Then graph the points. 5 1 25 2 1 0 1/5 -1

(5,1), (25, 2), (1, 0), (1/5, - 1)

Graph h(x) = ln(x + 2) y = ln(x + 2) ey = x + 2 ey – 2 = x Put 0 in for y e0 – 2 = x → 1 – 2 = x ( -1, 0) if x = 0, then y = ln(0 + 2) (0, ln 2); (0, 0.7) Since we know the basic shape, we might only need a few points

Graph of h(x) = ln( x + 2) There is a Vertical Asymptote at x = - 2. Why ?

Homework Page 216 – 218 # 3, 12, 17, 22, 26, 30, 35, 40, 44, 47, 59, 63, 68, 72

Homework Page 216 – 218 # 4, 14, 18, 23, 27, 32, 38, 43, 48, 64, 71