1. 1
 An example of an exponential function is:____________________________
 What would the inverse of that function look like?
 Now we need to solve for y. In order to change x b y to proper form, new
terminology had to be created by mathematicians.
Therefore the word ________________________ is used in place of exponent.
Exponential Form Logarithmic Form
 Graphing
Sketch y 2x Sketch the inverse of y 2x
y y
x x

2. 2
 y 2 x and ___________________ are inverses.
 x 2 y is equal to __________________, therefore, this is the graph of a
logarithmic function.
Graph (hint: convert to exponential form first)
f ( x) log3 x f ( x) log 1 x
2
y
y
x
x
Characteristics:
 Domain:__________________________
 Range:____________________________
 ________________________ function
 Common point: _____________ therefore, the x intercept would be __________.
 There is not a ____________. Therefore there is a vertical asymptote at ________
 If b > 1, the function is ___________________
 If 0 < b < 1, the function is ________________

3. 3
Sketch: f ( x) log 4 (3 x)
Hint: if you are using a table of values convert to exponential form first (switch and
factor).
x f(x) y
x
Interchanging Log and Exponential Forms
Log Form Exponential Form
log5 25 2
 Remember that y log a x
Evaluate:
1. y log9 27 hint: convert to exponential form and solve

4. 4
3
2. log b
4
3. log 2 (log3 9) x
FYI: Logs which are to the base of 10 are called __________________________
Calculators are set up to deal with base 10 logs. It is often written without the “10”
(x = log y)
Evaluate: log10 100
Without Calculator With Calculator

5. 5
Transformations:
State how each of the equations below transforms the graph of f ( x) loga x
1) f ( x) log2 ( x 1)
2) f ( x) log3 ( x 5)
3) f ( x) log 4 ( x) 3
4) f ( x) log5 ( x) 2
5) f ( x) log3 (1 x)
6) f ( x) log 2 (4 x) 1
7) f ( x) log 4 (3 x)
On Your Own
Sketch f ( x) log 4 (3 x) **Remember to change it to exponential form first!
4y x 4y x 3 y
x y x y
x

6. 6
On Your Own
Sketch f ( x) log 2 ( x 1) 3 **Remember to change it to exponential form first!
y
x