6.5 properties of logarithms - wordpress.com · 2018. 4. 6. · x = logb a, y = logbc, and z = logc...

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6.5 Properties of Logarithms Properties of Logarithms Example 1: Using Properties of Logarithms Use log $ 3 ≈ 1.585 and log $ 7 ≈ 2.807 to evaluate each logarithm. a) log $ . / b) log $ 21 c) log $ 49 Example 2: Expanding a Logarithmic Expression Expand ln 34 5 6 Example 3: Condensing a Logarithmic Expression Condense log 9 + 3 log 2 − log 3

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Page 1: 6.5 Properties of Logarithms - WordPress.com · 2018. 4. 6. · x = logb a, y = logbC, and Z = logc a.) CRITICAL THINKING Describe three ways to transform the graph off(x) = log x

6.5PropertiesofLogarithmsPropertiesofLogarithms

Example1:UsingPropertiesofLogarithmsUselog$ 3 ≈1.585andlog$ 7 ≈2.807toevaluateeachlogarithm.

a) log$ ./ b)log$ 21 c)log$ 49Example2:ExpandingaLogarithmicExpressionExpandln 34

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Example3:CondensingaLogarithmicExpressionCondenselog 9 + 3 log 2 − log 3

Page 2: 6.5 Properties of Logarithms - WordPress.com · 2018. 4. 6. · x = logb a, y = logbC, and Z = logc a.) CRITICAL THINKING Describe three ways to transform the graph off(x) = log x

Example4:ChangingaBaseUsingCommonLogarithmsEvaluatelog. 8usingcommonlogarithmsExample5:ChangingaBaseUsingCommonLogarithmsEvaluatelog9 24usingnaturallogarithmsExample6:ModelingwithMathematicsHomework:3,5,9-12,14-30even,33,34,43,44

Page 3: 6.5 Properties of Logarithms - WordPress.com · 2018. 4. 6. · x = logb a, y = logbC, and Z = logc a.) CRITICAL THINKING Describe three ways to transform the graph off(x) = log x

Page 4: 6.5 Properties of Logarithms - WordPress.com · 2018. 4. 6. · x = logb a, y = logbC, and Z = logc a.) CRITICAL THINKING Describe three ways to transform the graph off(x) = log x

Peirce, Regenerated Logc, Monist, 1896

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