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PRECALCULUS I

This resource outlines essential properties of logarithms and natural logarithms, emphasizing the change of base formula for positive real numbers. Key properties such as log multiplication, division, and exponentiation are covered thoroughly. Examples demonstrating the change of base, as well as expanding and condensing logarithmic expressions, provide practical applications. The guide concludes with an example to find the exact value of log 8.2, allowing learners to solidify their understanding of logarithmic concepts.

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PRECALCULUS I

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  1. PRECALCULUS I PROPERTIES OF LOGARITHMS Dr. Claude S. MooreDanville Community College

  2. CHANGE OF BASE for positive real numbers a, b, and x such that a¹ 1 and b 1.

  3. PROPERTIES OF LOGARITHMS 1. log b (uv) = log b u + log b v. 2. log b (u/v) = log b u - log b v. 3. log b un= n log b u.

  4. PROPERTIES OF NATURAL LOGARITHMS 1. ln (uv) = ln u + ln v. 2. ln (u/v) = ln u - ln v. 3. ln un= n ln u.

  5. EXPMPLE: CHANGE OF BASE

  6. EXAMPLE: EXPAND LOG EXPRESSION

  7. EXAMPLE: CONDENSE LOG EXPRESSIONS

  8. EXAMPLE: Find the exact value of log 8 2 .

  9. LET US WORK EXAMPLES.

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