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Mathematical Investigations III Name: Sample Test - Logs No Calculator Allowed 1. Evaluate: log5 (125) æ 1ö log 2 ç ÷ è 64 ø 2. Combine into a single logarithm then simplify. (Assume that all variables represent positive numbers.) a. 1 ln( x) 4 ln( xy ) 2 ln( y ). 2 b. 3log5 ( 2 x 4) 4log5 ( x 1) 2log5 (25 x ) 3. Solve for x: log 4 ( x) log 4 ( x 6) log 4 (16) . 4. Solve for x: 3·4 x+2 = 18. 5. Given the function f (x) = log3 (x + 2) - 5, find the inverse function f 1 ( x). 6. The half-life of a radioactive substance is 325 years. After how many years will the substance decay to 60% of its original amount? Leave your answer in terms of the natural log, ln( ). 7. Prove the following. Clearly show your steps to get full credit. log a (b 4 ) log a4 (b) . 16 8. Given p log3 (2) and q log3 (5) , express the following in terms of p, q if possible. 16 b. log 3 45 a. log3 log81 log 2 8 9. Solve for n in terms of a,b, and c: a b cn ac Log Test p.1 SP12 Mathematical Investigations III Name: 10. Graph each of the following functions. In each case label the scales on the x- and y- axes clearly and label at least three points. f ( x) log 2 (2 x) Domain = Range = f ( x) log2 x 1 Domain = Range = f ( x) log3 ( x 1) 2 Domain = Range = f ( x) log 3 ( x 2 ) Domain = Range = Log Test p.2 SP12