Section 7-5 Properties of Logarithms

Objectives I can evaluate Common Logs using a calculator I can use Change Base Rule I can expand log expressions using log properties I can condense log expressions using properties

Common Logarithms Your calculator has a button in the 7 th row called LOG. This button will calculate the base 10 common logarithm of a number. Example: log 125 = ROUND to 3 decimal places

Examples log 135 = 2.130

Change of Base Formula

Find: log 8 77.

Find: log

3 Main Properties Product Property Quotient Property Power Property

Product Property log b mn = log b m + log b n You can use this property from left to right or from right back to the left. Left to Right (Expanding) Right to Left (Condensing)

Product Rule log 2 4x = log log 2 x This is called expanding a log expression

Working Backwards log 3 x + log log 3 9 log 3 3x + log 3 9 log 3 27x This is called condensing an expression

Quotient Property log b m/n = log b m – log b n Left to Right (Expanding) Right to Left (Condensing)

Quotient Rule This is Expanding

Working Backwards log 3 x - log 3 3 log 3 x/3 This is called condensing an expression

Power Property log b m p = p log b m Left to Right (Expanding) Right to Left (Condensing)

Power Rule log 2 x 3 = 3log 2 x This is Expanding

Conversions

Condensing

Homework Worksheet 11-4