1. Properties of Logarithms
What you’ll learn
To use properties of logarithms
Define and use properties of logarithms to
simplify logarithmic expressions and to find the
approximate value
Use the change of base formula
Vocabulary
Change of base formula

2. Write a positive number on piece of paper.
Key this number to your calculator and press ENTER,
then perform the steps shown here, press ENTER
after each time. Do you recognize the results?
Try to explain why this result makes sense.
You get the number you started
with because every step that
changes the starting number is
undone by later steps.

3. Logarithms and exponents have corresponding properties.
Take a note:
Logarithms and exponents have corresponding
properties.
Definition of logarithm
Write mn as a product of powers
Product property of exponents
Definition of logarithm
Substitute for x and y

4. Problem 1: Simplifying Logarithms.
What is each expression written as a single logarithm?
Quotient Property
of logarithms
Divide
Write 16 as a power of 4
Simplify
Power property
of logarithms
Product property
of logarithms
Your turn
Answers

5. Problem 2: Expanding Logarithms What is each logarithm expanded?
Quotient and Product
property of logarithms
Answer:
Quotient and Product
property of logarithms
Answer:
729 as a power of 9
Your turn
Answers:

6. To evaluate a logarithm with any base, use the
Change of Base Formula.
Here is how it works

7. Problem 3: Using the Change of Base Formula
What is the value of each expression?
Method 1
Method 2
What common base has
powers that equals
27 and 81?
Use a calculator

8. 1. Use the Change of Base Formula.
Your turn
1. Use the Change of Base Formula.
What is the value of each expression?
Answers:
 2. The speed s (in mi/h) of the wind near the center of a tornado is related to the distance d (in miles) the tornado travels by s = 93 log d What was the difference in speed between a tornado that traveled 16 mi and one that traveled 8 mi?
Answer:
About 28mi/h

9. Write the equation for pH
Write the difference of pH levels
Solve and organize
Substitute the values
Use property of log and
simplify

10. Classwork odd Homework even
TB pgs exercises 9-74