Properties of Logarithms

Algebra 2

Evaluate Each Log

• log 1000

• log 103

• 3 log 10

• log (2000/2)

• log 2000 – log 2

Properties of Logs

• Product Property

• Quotient Property

• Power Property

Using Properties of Logs

• Use the following to evaluate each log

• log3 6

• log 3 24

• log 3 32

Expanding Log Expressions

• Expand:

• Write as a subtraction:• Write each term as an addition:

• Write each power as a multiplication:

Practice

• Expand:

• Write the expression in condensed form:log 9 + 3 log 2 – log 3

• Solution:

• Solution: log 24

Change of Base

• Change of Base Formula

• In particular:

Examples

• Evaluate log 3 8 using common logs and natural logs

• Solution:

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.

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?