MATH 115 Midterm: MATH 115 UPenn 115S03MupPost Exams
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Student no: answer all questions from section a, you may use a handwritten sheet of notes. Calculators are not permitted: read all questions carefully, unless explicitly told otherwise, you should explain all your answers fully, do not seperate the pages of your exam. Problem a1: [6 pts] (a) solve 3 x = 93+x for x. 9 = 32 so the equation becomes 3 x = 36+2x. |x 3| represents the distance of x from 3. |x 1| is the distance of x from 1. The set is therefore the set of points strictly closer to 1 than to 3, i. e. everything to the left of 2. The sets is the interval ( , 2). (c) simplify the following. Your answer should be an integer: log3 4 2 log3 6. Using the log laws log3 4 2 log3 6 = log3. = 2 (there are other equally valid ways to do this)
