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Properties of Logarithms

Section 5.3. Properties of Logarithms. Introduction. For a > 0, b > 0, b ≠ 1, the equations are equivalent. Property. Section 5.3. Slide 2. Exponential/Logarithmic Forms Property. Definition. Property. For x > 0, b > 0 and, b ≠ 1

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Properties of Logarithms

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  1. Section 5.3 Properties of Logarithms

  2. Introduction For a > 0, b > 0, b≠ 1, the equations are equivalent. Property Section 5.3 Slide 2 Exponential/Logarithmic Forms Property Definition

  3. Property For x > 0, b > 0 and, b≠ 1 In words: A logarithm of a power of x is the exponent times the logarithm of x. For positive real numbers a, b, and c where b≠ 1, the equations are equivalent. Property Section 5.3 Slide 3 Power Property for Logarithms Power Property for Logarithms and of Equality

  4. Example Solve the equation Check solution: Solution Section 5.3 Slide 4 Power Property for Logarithms Solving an Exponential Equation

  5. Warning Watch parenthesis: Section 5.3 Slide 5 Power Property for Logarithms Solving an Exponential Equation

  6. Example Solve Solution Section 5.3 Slide 6 Power Property for Logarithms Solving an Exponential Equation

  7. Solution Continued Check solution: Section 5.3 Slide 7 Power Property for Logarithms Solving an Exponential Equation

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