APC
Unit 4
Logarithmic Functions
Warm-up
 What
is the domain and range of an
exponential function


A) f(x) = 3x
B) g(x) = 2e(x-2)+3
 The
domain of a function is equal to the
__________ of its inverse function
 The range of a function is equal to the
___________ of its inverse function
Review Homework
 #54
(x)  (-x) reflect over y-axis
 (-3)  reflect over the x-axis and vertically
stretch x3
 (+9) Shift up 9 units

Key learnings
 Exponential
functions

Look for transformations that shift the graph
up or down
Moves the horizontal asymptote

Move the key point

 Starts
at (0,1)
#92
 Break
into 2 problems
 X<0
 X>0
is reflected over the y-axis
 The
power of a sketch
Activity – You Try it…
 text
Relating exponential and log
functions
Key Skill

Changing from Log form to equivalent
exponential form

The base of the log becomes the base of the
exponent

Remember this one to get the pattern

This is an equivalent equation

This is not the inverse
Evaluating Logrithms
 Set
the log equal to x
 Re-write
in exponential form
 Evaluate
the value of x that
 makes the equation true
Try Worksheet #2, 3, and 4
Calculator
 LOG
 LN
– log base 10
– Natural Log – Log base “e”
Try with and without your
Calculator
Transforming Log Functions
 Look

for transformation that shifts left/right
Moves the vertical asymptote
 Move

the key point
Starts at (1,0)
 Practice
Solving Logrithmic Equations
 Try
writing the equivalent exponential
equation

To get the variable out of the log( )
 Solve
for x
 Check your answers

No log of Negative numbers
Solving Logrithmic Equations
Problems from the homework
 To



evaluate log expressions
Remember to add = x
Write as an exponent
Then evaluate