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Mathematical Investigations III Name: Mathematical Investigations III Logarithms Practice 3 1. Solve for x. Leave answers rounded to four significant digits. 3x 4 12 5 g2 x 7 5x 18 a. b. c. 2. Evaluate, without a calculator. 1 a. log5 3 glog3 b. 5 8(log 2 3) c. log8 log2 log3 81 c. 32 log3 (x1) 3. Simplify. a. 4log4 (x3) b. log10 103x 1 4. 5. Find the inverse of each function. f x 2x 1 a. b. g x log 3 x 2 Write as the log of a single argument. 1 3log x log y 4log z 2 Logs 10.1 Rev. S12 Mathematical Investigations III Name: 6. A first-class postage stamp now costs $0.45. If we assume an annual rate of inflation of 2.8%, in what year would you expect a stamp to cost $0.60? 7. It was noted (Platt, 1984) that early statistics on the spread of the AIDS virus followed an exponential curve. In New York City alone, the cumulative number of people infected with the disease in 1983 was 1633 (New York Times, 16 March 1985). Over each of the next two years, the number grew by about 85%. If in fact, the spread of the disease had continued at that early, alarming rate, in what year would you have expected to find 1,000,000 people in NYC infected? Fortunately, through the help of education, this early rate has not continued. 8. $4,000 is deposited in a bank account at 5% interest per year, compounded monthly. How long will it take for the account to reach $10,000? 9. x 1 Prove: log9 log3 x 2 using two different methods. 81 2 a. Use the definition of logarithms. Begin b. Use log rules to rewrite and simplify the by writing the left side in exponential left side. form. Logs 10.2 Rev. S12