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HW14 Calc

# HW14 Calc - garcia(jjg2564 – HW 14 – gualdani –(56410...

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Unformatted text preview: garcia (jjg2564) – HW 14 – gualdani – (56410) 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 3 = 8 in equivalent logarithmic form. 1. log 8 2 = 3 2. log 2 1 8 = 3 3. log 2 8 =- 3 4. log 2 8 = 3 correct 5. log 10 8 = 2 Explanation: Taking logs to the base 2 of both sides we see that log 2 8 = log 2 2 3 = 3 log 2 2 . But log 2 2 = 1 , so log 2 8 = 3. 002 10.0 points Rewrite 3 log 2 x =- 4 in equivalent exponential form. 1. x 4 = 1 16 2. x 3 = 16 3. x 3 =- 9 4. x 4 = 9 5. x 3 = 1 16 correct Explanation: By exponentiation to the base 2, 2 3 log 2 x = 1 16 . But 2 3 log 2 x = 2 log 2 x 3 = x 3 . Hence the exponential form of the given equa- tion is x 3 = 1 16 . 003 10.0 points Use properties of logs to simplify the ex- pression log 7 ( x- radicalbig x 2- 14 ) + log 7 ( x + radicalbig x 2- 14 ) . 1. 1 + log 2 7 2. log 7 2 3. 1 + log 7 2 correct 4. log 2 7 5. 7 + log 7 2 Explanation: By properties of logs the given expression can be rewritten as log 7 braceleftBig ( x- radicalbig x 2- 14 ) ( x + radicalbig x 2- 14 ) bracerightBig = log 7 braceleftBig x 2- ( radicalbig x 2- 14 ) 2 bracerightBig . Thus the given expression reduces to log 7 14 = 1 + log 7 2 garcia (jjg2564) – HW 14 – gualdani – (56410) 2 since log 7 14 = log 7 7 + log 7 2 . 004 10.0 points Simplify the expression f ( x ) = 2 6(log 2 e ) ln x as much as possible. 1. f ( x ) = e 13 2. f ( x ) = 6 x 3. f ( x ) = x 6 correct 4. f ( x ) = x 2 5. f ( x ) = x 12 Explanation: By the property of inverse functions, 2 log 2 y = y, e ln y = y . Consequently, f ( x ) = 2 6(log 2 e ) ln x = (2 log 2 e ) 6 ln x = e ln x 6 = x 6 . 005 10.0 points Which one of the following could be the graph of f ( x ) = log 3 ( x- 2) when a dashed line indicates an asymptote? 1. 2. cor- rect 3. 4. 5. garcia (jjg2564) – HW 14 – gualdani – (56410) 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 ( x- 2) . Its graph will have a vertical asymptote at x = 2, and so will be that of log 3 ( x ) translated 2 units to the right. 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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HW14 Calc - garcia(jjg2564 – HW 14 – gualdani –(56410...

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