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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 =