1. 3.2 Logarithmic Function and their Graphs
How Exponential and Logarithm equations can be written in different forms

2. 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

4. 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

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

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

7. 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

8. 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
1/5 -1

9. (5,1), (25, 2), (1, 0), (1/5, - 1)

10. 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

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

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

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