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hw 14 solution

# hw 14 solution - silva(jrs4378 hW 14 gualdani(56455 This...

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silva (jrs4378) – hW 14 – gualdani – (56455) 1 This print-out should have 23 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Rewrite 2 4 = 16 in equivalent logarithmic form. 1. log 2 16 = 4 correct 2. log 2 1 16 = 4 3. log 16 2 = 4 4. log 10 16 = 2 5. log 2 16 = - 4 Explanation: Taking logs to the base 2 of both sides we see that log 2 16 = log 2 2 4 = 4 log 2 2 . But log 2 2 = 1 , so log 2 16 = 4. 002 10.0 points Rewrite 7 log 3 x = - 3 in equivalent exponential form. 1. x 3 = 1 27 2. x 7 = 27 3. x 7 = 1 27 correct 4. x 3 = 10 5. x 7 = - 10 Explanation: By exponentiation to the base 3, 3 7log 3 x = 1 27 . But 3 7log 3 x = 3 log 3 x 7 = x 7 . Hence the exponential form of the given equa- tion is x 7 = 1 27 . 003 10.0 points Use properties of logs to simplify the ex- pression log 5 ( x - radicalbig x 2 - 30 ) + log 5 ( x + radicalbig x 2 - 30 ) . 1. 1 + log 6 5 2. 5 + log 5 6 3. log 5 6 4. log 6 5 5. 1 + log 5 6 correct Explanation: By properties of logs the given expression can be rewritten as log 5 braceleftBig ( x - radicalbig x 2 - 30 ) ( x + radicalbig x 2 - 30 ) bracerightBig = log 5 braceleftBig x 2 - ( radicalbig x 2 - 30 ) 2 bracerightBig . Thus the given expression reduces to log 5 30 = 1 + log 5 6

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silva (jrs4378) – hW 14 – gualdani – (56455) 2 since log 5 30 = log 5 5 + log 5 6 . 004 10.0 points Simplify the expression f ( x ) = 3 8(log 3 e )ln x as much as possible. 1. f ( x ) = e 25 2. f ( x ) = x 3 3. f ( x ) = x 8 correct 4. f ( x ) = 8 x 5. f ( x ) = x 24 Explanation: By the property of inverse functions, 3 log 3 y = y, e ln y = y . Consequently, f ( x ) = 3 8(log 3 e )ln x = (3 log 3 e ) 8ln x = e ln x 8 = x 8 . 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. cor- rect 4. 5.
silva (jrs4378) – hW 14 – gualdani – (56455) 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 0 + 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 0 - 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)? 1. -8 -6 -4 -2 2 4 -4 -2 2 4 6 8 2. -8 -6 -4 -2 2 4 -4 -3 -2 -1 1 2

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silva (jrs4378) – hW 14 – gualdani – (56455) 4 3. -8 -6 -4 -2 2 4 -8 -6 -4 -2 2 4 4. -8 -6 -4 -2 2 4 -2 -1 1 2 5. -8 -6 -4 -2 2 4 -2 -1 1 2 3 4 correct Explanation: The graph of the function y = 1 - log 2 ( x + 8) can be obtained from the graph of the function y = log 2 x via the following procedure: (a) start with the graph of y = log 2 x ; (b) shift it by 8 units to the left; (c) next reflect it over the x -axis; (d) finally, shift the graph 1 unit up.
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hw 14 solution - silva(jrs4378 hW 14 gualdani(56455 This...

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