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Mathematical Investigations III Name: Mathematical Investigations III Logarithms Practice 5 1. Solve for x. a. log6 x 2 3 1 b. log 5log 7 log 9 x d. 3x 51.6 c. log8 3x 5 0 e. x 5 7 log 1 16 log 1 125 log 2 4 log5 25 2 2. 3 5 If the perimeter of the rectangle is no more than 6, determine the domain for x. log(x) log(20) 3. a. If f x 2 x 3 , find f 1 x . b. Logs 12.1 If g x log 3 x 2 ,find g 1 x . Rev. S07 Mathematical Investigations III Name: 4. Given isosceles trapezoid ABCD with AD = BC, AB log 9 8 , and EC log 9 72 log9(8) A a. Find DE. log8(81) E D b. Find the area of ABCD, and leave your answer simplified with log base 2. 5. Which is greater? Justify your answer. log(2) + log(4) + log(6) + log(8) or log(2 + 4 + 6 + 8) 6. Graph the following: (Watch the domains!) a. log y log 2x 6 B log9(72) C b. log y x c. log y log x log x 7. Explain why the graphs of y1 log x 2 and y2 2 log x are not the same. Logs 12.2 Rev. S07 Mathematical Investigations III Name: log x 1 2 x 4 8. Use graphing to solve for x: 9. a. Can a triangle exist with sides of length 2, 3, and 6? Why? b. Can a triangle exist with sides log(2), log(3), and log(6)? Why? c. Can a triangle exist with sides log(2), log(3), and log(5)? Why? 10. Given the graph of g, sketch the graph of the other functions. Label intercepts. yg x y g x yg x yg x3 1 yg x 11. y g x Solve for x. a. log3 log 2 x 2 b. log 2 log3 x 2 11. (continued) Logs 12.3 Rev. S07 Mathematical Investigations III c. Name: 10 log x x d. log x ln x e x e x . Find a so that f a 3 . 2 12. Let f x 13. Radioactive polonium has a half-life of 140 days. How many days will it take for 70% of a sample to decay? (Hint: Check the MI II exponential unit.) 14. A beverage company introduces a new soda, 6-Down Clear. During their big advertising campaign, revenue is about $200,000 per day. When the advertising stops, revenue begins to drop about 1.5% per day. They plan to start advertising again when revenue drops to $120,000. After how many days will this be necessary? Logs 12.4 Rev. S07