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Exponents, Logarithms, Sequences, and Series When you have completed your exam and reviewed your answers, click Submit Exam. Answers will not be recorded until you hit Submit Exam. If you need to exit before completing the exam, click Cancel Exam. Questions 1 to 20: Select the best answer to each question. Note that a question and its answers may be split across a page break, so be sure that you have seen the entire question and all the answers before choosing an answer. 1. Use properties of logarithms to expand the logarithmic expression below as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. A. ln e 3 + ln 11 B. 3 + ln 11 C. ln e 3 ? ln 11 D. 3 ? ln 11 2. Compute the value of A. 31 B. 36 C. 37 D. 30 3. Use summation notation to express the sum below. Use 1 as the lower limit of summation and i for the index of summation. A. B. C. D. 4. Write the first five terms of the arithmetic sequence below. a 1 = 15; d = ? 4 A. 15, 11, 6, 3, ? 1 B. 19, 15, 11, 7, 3 C. 11, 7, 3, ? 1, ? 5 D. 15, 11, 7, 3, ? 1 5. Find the sum, if it exists, of the infinite geometric series below: A. B. C. A sum doesn't exist for this geometric series. D. 6. Find the common ratio of the geometric sequence below: A. B. C. D. 7. Evaluate the expression below without using a calculator: log10 10,000 A. –4 B. 4 C. 40 D. 8. Which of these is not a valid fact about logarithms? A. b logb 1 = 1 B. y = logb x means b y = x C. logb b = 0 D. logb b x = x 9. Write the first four terms of the sequence defined by the following recursion formula: a 1 = ?3 and a n = ?2a n?1 for n ? 2 A. ? 3, ? 6, ? 12, ? 24 B. 3, ? 6, 12, ? 24 C. ? 3, 8, ? 14, 26 D. ? 3, 6, ? 12, 24 10. Use properties of logarithms to condense the logarithmic expression below to one term whose coefficient is 1. 2log y 4 + log y 2 A. log y 16 B. logy 32 C. log y 4 D. 2log y 8 11. Which of these is not a valid fact about logarithms? A. log2 7k = k log2 7 B. log2 (6 + k) = (log2 6) (log2 k) C. log2 1 = 0 D. log2 10/3 = log2 10 ? log2 3 12. Use properties of logarithms to expand the logarithmic expression below as much as possible. A. ln e 5 ? ln 9 B. 5 + ln 9 C. 5 ? ln 9 D. ln e 5 + ln 9 13. In a proof of by mathematical induction, an appropriate first step is to prove which of these statements? A. B. C. D. 14. Find the common ratio of the geometric sequence given below. A. B. C. D. 15. Make a table of coordinates for the function below and then graph it. f (x) = 5x A. B. C. D. 16. Which of the following statements is true about the number e? A. It’s the base of the natural logarithm. B. It’s equal to e e . C. It’s the base of every exponential function. D. It’s equal to 2p. 17. Evaluate the expression below to four decimal places. Use common logarithms or natural logarithms and a calculator. log4 28 A. 0.8451 B. 0.4160 C. 2.4037 D. 2.0492 18. Write the equation below in its equivalent logarithmic form. A. B. C. End of exam D. 19. Solve the logarithmic equation below. Be sure to reject any value that isn't in the domain of the original logarithmic expressions. Give the exact answer. log2 (x ? 2) = 3 A. {6} B. {7} C. {10} D. {11} 20. Find the accumulated value of an investment of $7,000 at 7% compounded continuously for 6 years. To solve question 3, use the correct formula for compound interest: A. $10,653.73 B. $9,940.00 C. $10,505.11 D. $10,753.73
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