hw 14 solution - silva (jrs4378) hW 14 gualdani (56455) 1...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 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 7 log 3 x = 1 27 . 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 = 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 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 ) 8 ln 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: Lets 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)?...
View Full Document

Page1 / 11

hw 14 solution - silva (jrs4378) hW 14 gualdani (56455) 1...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online