During this lesson, you will:
Write and evaluate logarithmic expressions
Graph logarithmic functions
Use logarithms in real-life situations

Evaluating Logarithmic Functions
We know that 2 2 = 4 and 2 3 = 8, but for what value of y does 2 y = 6? Because
2 2 < 6 < 2 3 , we would expect the answer between 2 and 3 question more precisely, mathematicians logarithms

Definition of Logarithm to Base b
The logarithm of y with base b is denoted by log log b y and is defined b as follows: y = x iff b x = y.
The expression log b y = x is read as
“log to the base b of y = x.”

Location of the Base and Exponent in
Logarithmic and Exponential Forms
Logarithmic Form: log b y = x
EXPONENT
BASE
Exponential Form:
EXPONENT b x = y
BASE
Note: A logarithm is an exponent .

Example 1 Rewriting Exponential and
Logarithmic Equations
Logarithmic Form log
2
16 log
10 log
Log log
3
1
10
2 log
6
3
10
4
0
= __________
= __________
0.1
=2.585
1/81 = -4 log
4
64 = 3 log
5
625 = 4 log
10
.001 = -3
Exponential Form
2 4 = 16
10 1 = 10
3 0 = 1
10 -1 = 1/10 =0.1
2
3
_____
-4
6
= _____
4 3 = _____
5 4 = _____
10 -3 = _____

ALERT! A logarithm is an exponent.
To evaluate log
3
9, you would ask
“____________________”?

Example 2 Evaluating Logarithms a. log
4
16 b. log
5
1 log
4
2
2 0 1/2 log
3
(-1) undefined

Not-So-Special Logarithmic
Values
Let a and x be positive number such that a ≠ 1,
1.log a
2. log a
Because: a 0 = 1
Because: a 1 = a
3. log a a x =______
Because: a x = a x

Example 3 Using a Calculator to
Evaluate a Logarithm log
2
Using the change of base formula, you can write log
2
6 = log
10 log
10
6 =
2 log

Day 1: Text, page 442 : 6-25 all,
50, 53-61 all. log
3
Plus, evaluate the following using a calculator:
20 log
4
7 log
1.4
10 log
6
(-3)