4.3 Logarithmic Functions and Graphs

Do NowFind 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 of is 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 GraphsWed 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