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# calc14 - pokharel(yp624 – HW14 – Radin –(56520 1 This...

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Unformatted text preview: pokharel (yp624) – HW14 – Radin – (56520) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Rewrite 6 log 2 x =- 4 in equivalent exponential form. 1. x 6 =- 9 2. x 6 = 16 3. x 4 = 9 4. x 6 = 1 16 correct 5. x 4 = 1 16 Explanation: By exponentiation to the base 2, 2 6 log 2 x = 1 16 . But 2 6 log 2 x = 2 log 2 x 6 = x 6 . Hence the exponential form of the given equa- tion is x 6 = 1 16 . 002 10.0 points Use properties of logs to simplify the ex- pression log 9 ( x- radicalbig x 2- 27 ) + log 9 ( x + radicalbig x 2- 27 ) . 1. 1 + log 9 3 correct 2. log 3 9 3. log 9 3 4. 9 + log 9 3 5. 1 + log 3 9 Explanation: By properties of logs the given expression can be rewritten as log 9 braceleftBig ( x- radicalbig x 2- 27 ) ( x + radicalbig x 2- 27 ) bracerightBig = log 9 braceleftBig x 2- ( radicalbig x 2- 27 ) 2 bracerightBig . Thus the given expression reduces to log 9 27 = 1 + log 9 3 since log 9 27 = log 9 9 + log 9 3 . 003 10.0 points Use properties of logs to simplify the ex- pression log a 8 + 3 5 log a 16- 3 5 log a 8 + log a 1 2 13 5 as much as possible. 1. log a 32 2. log a 8 3. log a 2 − 5 4. log a 2 correct 5. 2 Explanation: By properties of logs the given expression can be rewritten as pokharel (yp624) – HW14 – Radin – (56520) 2 log a braceleftBig 2 3 · 16 3 5 8 3 5 · 2 2 · 2 3 5 bracerightBig = log a 2 . 004 10.0 points Use the properties of logarithms to expand log 4 parenleftbigg x 5 y z 6 parenrightbigg . 1. log 4 5 x + log 4 y- log 4 6 z 2. 5 log 4 x + log 4 y- 6 log 4 z correct 3. log 4 x + 4 log 4 y- 6 log 4 z 4. 5 log 4 x + log 4 y + 6 log 4 z 5. log 4 5 x + log 4 y + log 4 6 z Explanation: log 4 parenleftbigg x 5 y z 6 parenrightbigg = log 4 ( x 5 y )- log 4 z 6 = log 4 x 5 + log 4 y- log 4 z 6 = 5 log 4 x + log 4 y- 6 log 4 z 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. 3. cor- rect 4. 5. pokharel (yp624) – HW14 – Radin – (56520) 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) ....
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calc14 - pokharel(yp624 – HW14 – Radin –(56520 1 This...

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