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HW2-solutions - wei(jw35975 HW2 milburn(54685 This...

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wei (jw35975) – HW2 – milburn – (54685) 1 This print-out should have 8 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points Determine which, if any, of f ( x ) = 256(16 - 2 x ) , g ( x ) = parenleftbigg 1 16 parenrightbigg 2 x - 2 , h ( x ) = 256(4 - 4 x ) , define the same function. 1. only g, f 2. only g, h 3. only f, h 4. none of f, g, or h 5. f, g, and h correct Explanation: By the laws of Exponents f ( x ) = 256(16 - 2 x ) = 16 2 (16 - 2 x ) = 16 2 - 2 x , while g ( x ) = parenleftbigg 1 16 parenrightbigg 2 x - 2 = 16 - (2 x - 2) = 16 2 - 2 x and h ( x ) = 256(4 - 4 x ) = 16 2 ( 4 2 ) - 2 x = 16 2 (16 - 2 x ) = 16 2 - 2 x Consequently, all of f, g, and h define the same function. 002 10.0points Find the solution of the exponential equa- tion 3 8 x = 9 5 2 x - 3 . 1. x = - 2 correct 2. x = 2 3. x = - 3 2 4. x = 3 2 5. none of these Explanation: By properties of exponents, 9 5 2 x - 3 = 3 5 x - 6 . Thus the equation can be rewritten as 3 8 x = 3 5 x - 6 , which after taking logs to the base 3 of both sides becomes 8 x = 5 x - 6 .
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