lesson38outline - MA 153 Lesson 38 Outline Quiz Solutions...

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MA 153 Lesson 38 Outline Quiz Solutions (Practice problems for distance learning students) 1. Change to log form: 4 log 1024 5 = 5 41 0 2 4 = 2. Find the number: 2 1 6 36 1 6 36 = = 6 1 log ____ 36 = 3. Solve the equation: 1 2 16 16 4 x x x = = = 16 1 log 2 x = Answering of homework questions over lesson 37. Lesson 38 Section 5.5 Properties of Logarithms If u and w are positive real numbers: (1) () log log log aa uw u w =+ a (2) lo g log log a u uw w ⎛⎞ =− ⎜⎟ ⎝⎠ (3) lo g log c uc u =
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Proof of the first property (#1): Let and log a ru = log a sw = Change both to exponential form: r au = s aw = Multiply the right sides and left sides: () log log log log rs a aa uw w uw r s uw u w + = = =+ a Example: Separate logs: (a) 1 2 2 log xy ⎛⎞ ⎜⎟ ⎝⎠ (b) ln x e (c) 3 24 log x w yz
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Example: Combine logs:
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lesson38outline - MA 153 Lesson 38 Outline Quiz Solutions...

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