8.5 Properties of Logarithms Goal: Use the properties of logarithms to evaluate, expand and condense logarithmic expressions.

Warm-up Simplify:

Properties of Logarithms Let b, m, and n be positive numbers such that b ≠ 1. Product Property Quotient Property Power Property

Example 1

Example 2 Expand the expression. Assume that all variables are positive.

Example 3 Condense the expression.

Loudness of a Sound Decibel LevelExample 130Jackhammer 110Dance club 90Lawn mower 70Television 50Rainfall 30Soft whisper 10Rustling leaf The loudness L of a sound (in decibels) is related to the intensity I of the sound (in watts per square meter) by the equation where I 0 is an intensity of watts per square meter, roughly the faintest sound that can be heard by humans. An air horn emits sound with an intensity I of 1 watt per square meter. Find its decibel level.

Loudness of a Sound How much louder is the sound of 5 air horns, compared to just one air horn? So 5 air horns would be approximately 7 decibels more.

Change of Base Formula Logarithms with any base other than 10 or e can be written in terms of common or natural logarithms using the change-of-base formula. This allows you to evaluate any logarithm using a calculator. Change of Base Formula If a, b, and c are positive numbers with b ≠ 1 and c ≠ 1, then: In particular, and

Example Evaluate:

Assignment Worksheet 8.5