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LOGARITHMIC FUNCTION. Learning objectives: (1) change exponential…
LOGARITHMIC FUNCTION
. Learning objectives: (1) change exponential statements to logarithmic statements and logarithmic statement to exponential statements, (2) evaluate logarithmic expressions, (3) determine the domain of a logarithmic function, (4) graph logarithmic functions, (5) solve logarithmic equations
1. Definition of Logarithmic function
see
http://gg.gg/deflog
2. Change Exponents statements to Logarithmic Statements and Logarithmic Statements to Exponents statements
Example 1: change each exponential statement to an equivalent statement involving a logarithm.
Answer Example 1:
http://gg.gg/answerexample1
Example 2: change each logarithmic statement to an equivalent statement involving an exponential
Answer Example 2:
http://gg.gg/answerexample2
3. Evaluate logarithmic Expressions
Example 3: Find the exact value of :
Answer Example 3:
http://gg.gg/answerexample3
4. Determine the domain of a logarithmic function
Domain Log function = range of Exponents function =
Range log function = Domain of Exponents function =
Example 4: find the domain of each logarithmic function:
Answer Example 4:
http://gg.gg/answerexample4
Example 4* : find the domain of each logarithmic function:
Answer example 4* :
http://gg.gg/answerexample4-1
5. Graph Logarithmic Function
. Go to
http://gg.gg/graphlog
properties Graph of Logarithmic function
http://gg.gg/propgraphlog
Natural Logarithm function
graph of natural log function
http://gg.gg/graphnaturallog
Example 5 :
http://gg.gg/example5
answer:
http://gg.gg/answer5
and
http://gg.gg/answer5-2
Example 6:
http://gg.gg/example-6
answer:
http://gg.gg/answer6-1
,
http://gg.gg/answer6-2
and the graph
http://gg.gg/answer6-3
6. Solving Logarithmic Equation
Example 7: Find solution of
answer example 7 :
http://gg.gg/answerexample7
Steps: (1) Changing to exponential form, (2) checking the answer
Using Logarithms to solve an exponential function (by change to logarithmic form)
Example 8: Solve
Answer Example 8:
http://gg.gg/answerexample8
7. SUMMARY
:
http://gg.gg/summary-log
8. CONCEPT AND VOCABULARY
The domain of the logarithmic function
is ....
the graph of every logarithmic function
, where
, passes through three points : ...., ...., and ....
if the graph of a logarithmic function
, where
, is increasing, then its base must be larger than ....
True or False
. If
, then
True of False
. The graph of
, where
, has an x-intercept equal to 1 and no y-intercept.
9. ASSIGNMENT
:
http://gg.gg/assignmentlogfunction
