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10/27/2014 3.3: Properties of Logarithms College Algebra/Pre-Calculus “I can . . .” Use the product rule.” Use the quotient rule.” Use the power rule.” Expand logarithmic expressions.” Condense logarithmic expressions.” Use the change-of-base property.” Product Rule: • Let b, M, and N be positive real numbers with b ≠ 1. = + • Ex. 1: Expand the logarithmic expression. ( ∙ ) → () → 1 10/27/2014 Quotient Rule: • Let b, M, and N be positive real numbers with b ≠ 1. • Ex. 2: Expand the logarithmic expression. ( ) → ( ) → Power Rule: • Let b and M be posiƟve real numbers with b ≠ 1, and let p be any real number. = • Ex. 3: Expand the logarithmic expression. → → ( + ) → 2 10/27/2014 Expanding Logarithmic Expressions: Ex. 4: Use properties to expand each expression as much as possible. Where possible, evaluate logarithmic expressions without the using a calculator. a) ( ) b) ( ) Expanding Logarithmic Expressions: Ex. 4: Use properties to expand each expression as much as possible. Where possible, evaluate logarithmic expressions without the using a calculator. ] c) [ d) 3 10/27/2014 Condensing Logarithmic Expressions: Ex. 5: Use properties to condense each expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without the using a calculator. a) ! + − ! b) + Condensing Logarithmic Expressions: Ex. 5: Use properties to condense each expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without the using a calculator. c) + + d) − − 4 10/27/2014 Change of Base Property: Common Logarithms: = Natural Logarithms: = # # Change of Base: Ex. 6: Use common logarithms or natural logarithms to evaluate to four decimal places. a) b) $ 5 10/27/2014 3.3 Properties of Logarithms Practice Problems: Page 449: 3-78 mult. of 3 Timeline: • Fri. (10/31): • 3.2 Quiz • 3.5 Notes • Tues. (11/4): • 3.3 Quiz • 3.4 Notes • Thurs. (11/6): • 3.5 Quiz • 4.1 Notes • Mon. (11/10): • 3.4 Quiz • 4.2 Notes • Wed. (11/12): • CHAPTER 3 TEST 6