3.2 Logarithmic Functions and Graphs

Vocab: Logarithmic functions, base, properties of logs, transformations, Natural logarithmic function, Domain

OBJECTIVES: • Recognize and evaluate logarithmic

functions with base a. • Graph logarithmic functions • Recognize, evaluate, graph natural log

functions • Model and solve real life problems

3.1 Definition of Logarithmic Functions in base a

What is a Logarithmic Function?

The logarithmic function is the inverse function of the exponential Function.

3.2 Definition of Logarithmic Function

What is The defn. Of logarithmic Function?

How do I evaluate Log functions?

One to one property

How do I use The one-to-one Property to solve A logarithmic Function?

Ex. Solve the following using the one-to-one property:

Properties of Logarithmic Functions

What are the Properties?

Transformations of Logs

How do I describe transformations of an logarithmic graph?

Ex. Describe the transformations from f(x) = log₃ x: Graph log₃x in y₁ a. To g(x) = log₃ x - 1

b. To h(x) = log₃ (x + 2)

c. To k(x) = - log₃ x

Remember: if it is with x, it is a horizontal change, and it is opposite of the sign, if it is with y, or f(x), it is a vertical change and it is normal.

The Natural Log Function y = lnx and y=𝑒𝑥 are inverses Function defined by f(x) = logₑx= lnx, x>0

Evaluate lnx, if: A. x=2 B. x=.3 C. x=-1

Properties of Natural Logarithmic Functions

What are the Properties?

Simplify:

a. ln𝑒13

b. 5ln(1)

c. 𝑒𝑙𝑛7

Graph of Natural Logarithmic Functions

How do we graph and find Domain, range, Asympotes?

Graph f(x) = ln(x)

Domain of (0,∞) with a vertical Asymptote of x = 0

Ex. Graph f(x) = ln(x-2) and find domain. Domain of ( , ) with a vertical Asymptote of x =