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# Review 3 - MAC 1147 Review 3 Fall 2009 Exam 3 covers...

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MAC 1147 Review 3, Fall 2009 Exam 3 covers Lectures 19-27 1. Solve the system: (a) 2 x 3 y = 2 3 x 2 y = 12 (b) x 2 + y 2 = 17 3 y x = 1 (c) 8 < : 1 2 x 2 3 y = 2 3 x + 4 y = 12 2. Sketch the graph of the function f ( x ) = 2 e ( x +1) . Find its domain, range, asymptote and at least one point. Is the function increasing or decreasing? 3. Find the domain, range, asymptote, intercepts and sketch the graph of the function y = 2 2 log 2 ( x + 1). 4. Evaluate: (a) log 25 5 (b) log 2 1 2 (c) log 100 (c) ln e 3 (e) log 1 3 81 5. Simplify, where it is possible. Give all restrictions on the variables: (a) log 3 9 log 5 25 (b) e 3 ln x (c) log 10 2 x 2 (d) log 4 2 x 2 (e) 5 log 3 x (f) ln( x 2 + y 2 ) 6. Write as a single logarithm: 5 log 2 3 log x + 2 log y log 3 7. Rewrite ln e 2 p xy p y z 2 as a sum and/or di erence of logarithms. 8. Solve the exponential equations: 9. Solve the logarithmic equations: (a) log 2 ( x 3) 2 = 4 (b) log 3 (2 x + 1) log 3 ( x 1) = 2 (c) ln x + ln( x 2) = ln 3 (d) log 3 p x 6 = 2 10. Let = 230 .

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