# L21 - Lecture 21: Section 3.2 Logarithmic Functions Recall...

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Unformatted text preview: Lecture 21: Section 3.2 Logarithmic Functions Recall the graph of exponential function u1D453 ( u1D465 ) = u1D44E u1D465 , u1D44E &gt; 1: (0,1) Since u1D453 ( u1D465 ) is one-to-one, it has an inverse function. Def. The logarithmic function with base u1D44E , where u1D44E &gt; 0 and u1D44E = 1 is written u1D453 ( u1D465 ) = log u1D44E u1D465 and is defined by the relationship u1D466 = log u1D44E u1D465 if and only if ex. Write in exponential form: 1) log 3 uni0028.alt03 1 9 uni0029.alt03 = 2 2) log u1D452 (3 u1D465 + 1) = 2 ex. Write in logarithmic form: 4 1 . 5 = 8 ex. Evaluate: 1) log 2 64 = 2) log 3 1 = 3) log 3 3 = 4) log 10 uni0028.alt03 1 1000 uni0029.alt03 = 5) log 16 4 = 6) log 2 ( 1) = 7) log 2 0 = Properties of Logarithms 1. Recall: If u1D466 = log u1D44E u1D465 , then u1D465 = That is, u1D465 &gt; 0. 2. log u1D44E 1 = 3. log u1D44E u1D44E = 4. Inverse Properties: log u1D44E u1D44E u1D465 = for all real number u1D465 u1D44E log u1D44E u1D465 = for u1D465 &gt; 5. One-to-One Properties:...
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## L21 - Lecture 21: Section 3.2 Logarithmic Functions Recall...

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