L22 - Lecture 22 Section 3.3 Properties of Logarithms...

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Unformatted text preview: Lecture 22: Section 3.3 Properties of Logarithms Recall the following properties of Logarithm: The logarithmic function with base u1D44E u1D466 = u1D453 ( u1D465 ) = log u1D44E u1D465 if and only if 1. Domain of u1D453 : 2. log u1D44E 1 = 3. log u1D44E u1D44E = 4. log u1D44E u1D44E u1D465 = for all real number u1D465 u1D44E log u1D44E u1D465 = for u1D465 > The Natural Logarithmic Function u1D466 = ln u1D465 if and only if Note the following: ln 1 = ln u1D452 = u1D452 ln u1D465 = ln( u1D452 u1D465 ) = Properties of Logarithms Let u1D462, u1D463 and u1D44E be positive real numbers with u1D44E ∕ = 1 and u1D45B be any real number. The following properties hold: 1. log u1D44E ( u1D462u1D463 ) = 2. log u1D44E uni0028.alt02 u1D462 u1D463 uni0029.alt02 = 3. log u1D44E u1D462 u1D45B = Proof: NOTE: log u1D44E ( u1D462 + u1D463 ) ∕ = log u1D44E u1D462 + log u1D44E u1D463 (log u1D44E u1D462 ) u1D45B ∕ = u1D45B log u1D44E u1D462 ex. Evaluate: 1) log 4 2 + log 4 32 2) log 2 80 − log 2 5 3) −...
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L22 - Lecture 22 Section 3.3 Properties of Logarithms...

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