Determine if the following statements are true or false...

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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. 2. Express in simplest form: log 5 .
5 125 w
3. Solve for x in each of the following equations. (a) e 4 x - 1 = 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 + 3 x = 4( x + 5) x 2 + 3 x = 4 x + 20 x 2 + 3 x - 4 x - 20 = 0 x 2 - x - 20 = 0 ( x + 4)( x - 5) = 0 Hence, x = - 4 , 5 . (c) 2 3 x = 10 Sol. 2 3 x = 10 log(2 3 x ) = log(10) 3 x log 2 = 1 3 x = 1 log 2 x = 1 3 log 2
(d) 9 x +1 = 81 1 - 3 x

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