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Properties of Logarithms

Explore the fundamental properties of logarithms, including the power, product, and quotient properties. This guide covers key rules applicable for positive values of a, b, and m (where m ≠ 1), as well as any real number n. Learn how to condense expressions and expand them, with practical examples demonstrating each property. Understand the importance of proper placement of addition/subtraction and multiplication/division in logarithmic expressions for effective simplification.

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Properties of Logarithms

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  1. Properties of Logarithms

  2. Properties of Logarithms For a>0, b>0, m>0, m≠1, and any real number n. Power Property: Product Property: Quotient Property:

  3. Example 1 Condense the expression:

  4. Example 2 Expand the expression:

  5. Example 3 A) Expand the expression: Addition/Subtraction must be outside the log. B) Condense the expression: Multiplication/Division must be inside the log.

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