4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1

Logarithmic Functions A logarithmic function is the inverse of an exponential function It behaves similarly to an exponential function

Logarithmic Functions as an Inverse The inverse ofis given by We convert between the 2 equations when evaluating logarithms

Ex Find each of the following: 1) 2) 3) 4) 5) 6)

Ex Convert each of the following to a logarithmic equation 1) 2) 3)

Ex Convert to an exponential equation 1) 2) 3)

Logarithms and Calculators Logarithms can be evaluated on calculators – We can evaluate base 10 (LOG) and base e (LN) logarithms using our calculators To convert logarithms, we need to use the change of base formula

Changing Logarithmic Bases For any logarithmic bases a and b, and any positive number M,

Ex Evaluate using the change of base formula

Closure Evaluate without a calculator HW: p.387 #9-77 odds

4.3 Logarithmic Graphs Wed April 8 Do Now Evaluate the following without a calculator 1) 2)

HW Review: p.387 #9-77

Graphs of Logarithmic Functions Since logarithms are inverses of exponential functions, the following are true: – The x-intercept is (1,0) – There is a vertical asymptote at x = 0 – The domain is all positive numbers – The range is all real numbers If you want to graph on the calculator, you must use the change of base formula and graph that

Ex Graph

Ex Graph each of the following. Describe how each graph can be obtained from the basic function graph 1) 2) 3)

Applications Ex 12 and 13 in book p.384

Closure Graph HW: p.387 #79-97 odds