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Unformatted text preview: handa (nh5757) Exponentials (1.5) bormashenko (54880) 1 This printout should have 10 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points Find the solution of the exponential equa tion 4 7 x = 16 1 2 x +6 . 1. x = 2 correct 2. x = 2 3. x = 12 7 4. x = 12 7 5. none of these Explanation: By properties of exponents, 16 1 2 x +6 = 4 x +12 . Thus the equation can be rewritten as 4 7 x = 4 x +12 , which after taking logs to the base 4 of both sides becomes 7 x = x + 12 . Rearranging and solving we thus find that x = 2 . 002 10.0 points Find x when 2 x = 8 y , 4 x = 16 y 1 . 1. x = 6 correct 2. none of these 3. x = 6 4. x = 2 5. x = 2 Explanation: The equations 2 x = 8 y , 4 x = 16 y 1 are equivalent to 2 x = 2 3 y , 2 2 x = 2 4( y 1) . Now set v = 2 x and u = 2 y . Then v = u 3 , v 2 = 1 16 u 4 . Substituting for u in the second equation we thus get v 2 = 1 16 v 4 3 , i . e ., v = 2 6 . Consequently, since v = 2 x , x = 6 . 003 10.0 points Determine which, if any, of the following f ( x ) = 25 x + 10 , g ( x ) = 5 2 x +2 , h ( x ) = 25(25...
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This note was uploaded on 11/21/2011 for the course M 408N taught by Professor Gualdini during the Spring '10 term at University of Texas at Austin.
 Spring '10
 Gualdini

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