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Properties of Logarithms

Properties of Logarithms. Objectives: Work with the Properties of Logarithms Write a Logarithmic Expression as a Sum or Difference of Logs Write a Logarithmic Expression as a Single Log Evaluate Logarithms whose Base is neither 10 nor e. The Product Rule: The Quotient Rule:

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Properties of Logarithms

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  1. Properties of Logarithms Objectives: Work with the Properties of Logarithms Write a Logarithmic Expression as a Sum or Difference of Logs Write a Logarithmic Expression as a Single Log Evaluate Logarithms whose Base is neither 10 nor e

  2. The Product Rule: • The Quotient Rule: • The Power Rule: • The Change-of-Base Property: • Exponent Rules Properties of LogarithmsLet be positive real numbers with and be any real number

  3. To expand a logarithmic expression, we write a single logarithm as the sum or difference of two or more logarithmic expressions and we pull the exponent to the front.To condense a logarithmic expression, we write the sum or difference of two or more logarithmic expressions as a single logarithmic expression. Coefficients of logarithms must be 1 before you can condense them using the product and quotient rules • 1. • 2.

  4. 3. • 4. • EXPAND 5.6.CONDENSE

  5. 4. 5. 6. EX: Use properties of logarithms to find the exact value of each expression. Do not use a calculator.1. 2. 3.

  6. EX: Use the Change-of-Base formula and a calculator to approximate each logarithm. Round your answer to the three decimal places. • a) b) EX: Suppose that . Use the properties of logarithms to write each log in terms ofa) b)

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