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Unformatted text preview: mandel (tgm245) – HW14 – Radin – (56470) 1 This printout should have 23 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Rewrite 3 2 = 9 in equivalent logarithmic form. 1. log 3 9 = 2 correct 2. log 9 3 = 2 3. log 10 9 = 3 4. log 3 1 9 = 2 5. log 3 9 = 2 Explanation: Taking logs to the base 3 of both sides we see that log 3 9 = log 3 3 2 = 2 log 3 3 . But log 3 3 = 1 , so log 3 9 = 2. 002 10.0 points Rewrite 7 log 3 x = 2 in equivalent exponential form. 1. x 7 = 1 9 2. x 7 = 9 correct 3. x 7 = 7 4. x 2 = 9 5. x 2 = 7 Explanation: By exponentiation to the base 3, 3 7 log 3 x = 9 . But 3 7 log 3 x = 3 log 3 x 7 = x 7 . Hence the exponential form of the given equa tion is x 7 = 9. 003 10.0 points Use properties of logs to simplify the ex pression log 8 ( x radicalbig x 2 24 ) + log 8 ( x + radicalbig x 2 24 ) . 1. log 8 3 2. 1 + log 8 3 correct 3. log 3 8 4. 8 + log 8 3 5. 1 + log 3 8 Explanation: By properties of logs the given expression can be rewritten as log 8 braceleftBig ( x radicalbig x 2 24 ) ( x + radicalbig x 2 24 ) bracerightBig = log 8 braceleftBig x 2 ( radicalbig x 2 24 ) 2 bracerightBig . Thus the given expression reduces to log 8 24 = 1 + log 8 3 mandel (tgm245) – HW14 – Radin – (56470) 2 since log 8 24 = log 8 8 + log 8 3 . 004 10.0 points Simplify the expression f ( x ) = 2 3(log 2 e ) ln x as much as possible. 1. f ( x ) = e 7 2. f ( x ) = x 3 correct 3. f ( x ) = x 2 4. f ( x ) = 3 x 5. f ( x ) = x 6 Explanation: By the property of inverse functions, 2 log 2 y = y, e ln y = y . Consequently, f ( x ) = 2 3(log 2 e ) ln x = (2 log 2 e ) 3 ln x = e ln x 3 = x 3 . 005 10.0 points Which one of the following could be the graph of f ( x ) = log 3 parenleftBig 1 x 4 parenrightBig when a dashed line indicates an asymptote? 1. 2. 3. 4. 5. cor rect mandel (tgm245) – HW14 – Radin – (56470) 3 6. Explanation: Let’s first review some properties of ln x and ln( x ). Since ln x is defined only on (0 , ∞ ) and lim x → + ln x =∞ , lim x →∞ ln x = ∞ , the graph of ln x has a vertical asymptote at x = 0 and so is given by But then ln( x ) is defined only on (∞ , 0) and has the properties lim x → ln( x ) =∞ , lim x →−∞ ln( x ) = ∞ , so its graph has a vertical asymptote at x = 0 and is given by Now the given function is f ( x ) = log 3 parenleftBig 1 x 4 parenrightBig = log 3 ( x 4) . Its graph will have a vertical asymptote at x = 4, and so will be that of log 3 ( x ) translated 4 units to the left, then ‘flipped over’ the x axis. Consequently, f has graph keywords: LogFunc, LogFuncExam, 006 10.0 points Which of the following is the graph of the function y = 1 log 2 ( x + 8)?...
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This note was uploaded on 06/14/2011 for the course MATH 305G taught by Professor Cathy during the Spring '11 term at University of Texas at Austin.
 Spring '11
 Cathy

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