CHAPTER_ppt_12_5

CHAPTER_ppt_12_5 - 12.5 Properties of Logarithms Properties...

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§ 12.5 Properties of Logarithms

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Martin-Gay, Beginning and Intermediate Algebra, 4ed 2 Properties of Logarithms This section examines several properties of logarithms that allow you to simplify expressions. Recall that a logarithm is an exponent, so logarithmic properties are restatements of exponential properties.
Martin-Gay, Beginning and Intermediate Algebra, 4ed 3 Product Property of Logarithms If x , y , and b are positive real numbers and b ≠ 1, then log b xy = log b x + log b y. Note that although the property allows you to split the logarithm of a product into the sum of two logarithms, we usually use the property to consolidate a sum of logarithms into a single logarithm. Product Property

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Martin-Gay, Beginning and Intermediate Algebra, 4ed 4 Write each expression as a single logarithm. 1) log 7 x + log 7 4 log 7 4 x 1) log z 5 + log z 8 log z 40 1) log 2 x + log 2 10 + log 2 ( x + 3) log 2 10 x ( x + 3) Product Property Example:
Martin-Gay, Beginning and Intermediate Algebra, 4ed

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CHAPTER_ppt_12_5 - 12.5 Properties of Logarithms Properties...

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