2. Section 12.3 Logarithmic Functions

3. Review 2 = 4 2 = 8 2 = 13 2 = 16 3 2 4 3.7 This is a pretty good approximation to the answer, but it is not the EXACT answer. We can never write down all the correct digits of this exponent  We were led to invent the Logarithm notation

4. Definition of Logarithm the exponent to which a must be raised to obtain b is We read “log base a of b”

5. 2 because = 3 10 3 = 1000 5 0 = 1 0 because a 3 2 = 9 c c b Examples

6. Logarithmic and Exponential Forms c a c = b base Logarithmic formExponential Form

7. Consider a new function xy=f(x) 1/8 1/4 1/2 1 2 4 8

8. Consider a new function xy=f(x) 1/8-3 1/4-2 1/2 10 21 42 83

9. Observe these 2 functions xy=g(x) -31/8 -21/4 1/2 01 12 24 38 xy=f(x) 1/8-3 1/4-2 1/2 10 21 42 83 f(x) is the inverse of g(x)

10. Graph of logarithmic Function y = x

11. Logarithmic Functions Logarithmic Function is the inverse function of exponential function. 1. The domain is (0, ∞). 2. The range is the interval (−∞, ∞). 3. The graph has a x-intercept of (1, 0). 4. The y-axis is called an asymptote of the graph.