This document discusses logarithmic functions and their inverses, exponential functions. It provides examples of logarithmic and exponential forms and how to convert between them. It also covers graphing logarithmic functions, their domains and ranges, characteristics like asymptotes. It provides examples of evaluating logarithmic expressions and transformations of logarithmic functions.

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