1. Properties of Logarithms
Algebra 2

2. Evaluate Each Log
• log 1000
• log 103
• 3 log 10
• log (2000/2)
• log 2000 – log 2

3. Properties of Logs
• Product Property
• Quotient Property
• Power Property

4. Using Properties of Logs
• Use the following to evaluate each log
• log3 6
• log 3 24
• log 3 32

5. Expanding Log Expressions
• Expand:
• Write as a subtraction:
• Write each term as an addition:
• Write each power as a multiplication:

6. Practice
• Expand:
• Write the expression in condensed form:
log 9 + 3 log 2 – log 3
• Solution:
• Solution: log 24

7. Change of Base
• Change of Base Formula
• In particular:

8. Examples
• Evaluate log 3 8 using common logs and
natural logs
• Solution:

9. Log Example
• For sound with intensity I (in watts per square
meter), the loudness L(I) of a sound (in
decibels) is given by the function:
• Where I0 is barely audible sound.

10. Log Example
• An artist is a studio turns up the volume on a
track so that the sound’s intensity doubles.
How many decibels does the sound level
increase?