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Mastering Properties of Logarithms: Equations, Power, and Solutions

Explore the essential properties of logarithms, including equations, power property, and solving methods. Understand how to solve exponential equations accurately and efficiently. Learn through examples and solutions to enhance your mathematical skills.

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Mastering Properties of Logarithms: Equations, Power, and Solutions

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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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