Section 12.3 Logarithmic Functions

Review 2 = 4 2 = 8 2 = 13 2 = 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

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

2 because = = = 1 0 because a 3 2 = 9 c c b Examples

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

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

Consider a new function xy=f(x) 1/8-3 1/4-2 1/

Observe these 2 functions xy=g(x) -31/8 -21/4 1/ xy=f(x) 1/8-3 1/4-2 1/ f(x) is the inverse of g(x)

Graph of logarithmic Function y = x

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.