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Exponentials (1.5)-solutions- HW1

Exponentials (1.5)-solutions- HW1 - handa(nh5757...

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handa (nh5757) – Exponentials (1.5) – bormashenko – (54880) 1 This print-out should have 10 questions. Multiple-choice 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 x ) , define the same function.
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