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Introduction to Logarithms

Introduction to Logarithms. Chapter 8.4. Logarithmic Functions. log b y = x if and only if b x = y. Logarithmic Form log 2 32 = 5. Exponential Form 2 5 = 32. ( ) -1 = 2. 1 2. Rewriting Logarithmic Equations. log 5 1 = 0. 5 0 = 1. log 10 10 = 1. 10 1 = 10.

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Introduction to Logarithms

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  1. Introduction to Logarithms Chapter 8.4

  2. Logarithmic Functions logby = x if and only if bx = y

  3. Logarithmic Form log232 = 5 Exponential Form 25 = 32 • ( )-1 = 2 1 2 Rewriting Logarithmic Equations • log51 = 0 • 50 = 1 • log1010 = 1 • 101 = 10 • log½2 = -1

  4. Special Logarithmic Values • Logarithm of 1 logb1 = 0 because b0 = 1 • Logarithm of Base b logbb = 1 because b1 = b

  5. Evaluating Logarithmic Expressions • Evaluate log381 3 to what power gives 81? 34 = 81, therefore log381 = 4

  6. The Common Logarithm • The logarithm with base 10 is called the common logarithm. • It is denoted log10 or simply log. • The log button on your calculator evaluates common logarithms.

  7. logbu logbc log u logc Change of Base Formula • Let u, b, c be positive numbers b  1 and c  , logcu = • So to convert expressions to common logarithms in order to use your calculator • logcu =

  8. Properties of Logarithms Let b, u , and v be positive and b  1 • Product Property logbuv = logbu + logbv • Quotient Property logb = logbu – logbv • Power Property logbun = n logbu u v

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