Q8SOL - MAP 103: Proficiency Algebra, Quiz #8, Fall 2009...

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Unformatted text preview: MAP 103: Proficiency Algebra, Quiz #8, Fall 2009 SOLUTIONS 1. Determine if the following statements are true or false. You do not need to justify your answer. (a) T | F : e x e x = e 2 x (b) T | F : f ( x ) = 2 x +1 + 1 has translated intercept (1 , 2) (c) T | F : ln( a ) + ln( b ) = ln( a + b ) for every a,b > (d) T | F : log 2 1 + log 2 2 + log 2 2 2 = 3 (e) T | F : log(4) + ln( e ) = 2 log 2 + 1 2. Express in simplest form: log 5 5 r x 5 y 25 z 125 w ! . Sol. = 1 5 [log 5 ( x 5 y 25 z )- log 5 (125 w )] = 1 5 [log 5 ( x 5 ) + log 5 ( y 25 ) + log 5 ( z )- log 5 (125)- log 5 ( w )] = 1 5 [5 log 5 x + 25 log 5 y + log 5 z- 3- log 5 w ] = log 5 x + 5 log 5 y + 1 5 log 5 z- 3 5- 1 5 log 5 w 3. Solve for x in each of the following equations. (a) e 4 x- 1 = 0 Sol. e 4 x- 1 = 0 e 4 x = 1 ln( e 4 x ) = ln 1 4 x = 0 x = 0 (b) log 4 ( x 2 + 3 x )- log 4 ( x + 5) = 1 Sol. log 4 ( x 2 + 3 x )- log 4 ( x + 5) = 1 log 4 x 2 + 3 x x + 5 = 1 4 log 4 h x 2 +3 x x +5 i = 4 1 x 2 + 3 x x + 5 = 4 x 2...
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Q8SOL - MAP 103: Proficiency Algebra, Quiz #8, Fall 2009...

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