1. Find the exact value of the logarithmic expression ln e. a. 0 b. -1 c. 1 d. e Q2. The graph of an exponential function is given. Match the graph to one of the following functions. a. f(x) = 3x b. f(x) = -3x c. f(x) = 3-x d. f(x) = -3-x Q3. Find the exact value of the logarithmic expression log a. -1/3 4 1/64. b. -3 c. 1/3 d. 3 Q4. Solve the equation log a. {-7} 4 (x + 2) = -1 b. {-7/4} c. {9/4} d. {9} Q5. Find the inverse of the function and state its domain and range. {(-3, 4), (-1, 5), (0, 2), (2, 6), (5, 7)} a. {(3, 4), (1, 5), (0, 2), (-2, 6), (-5, 7)}; D = {3, 1, 0, -2, -5}; R = {2, 4, 5, 6, 7} b. {(-3, -4), (-1, -5), (0, -2), (2, -6), (5, -7)}; D = {-3, -1, 0, 2, 5}; R = {-7, -6, -5, -4, -2} c. {(4, -3), (5, -1), (2, 0), (6, 2), (7, 5)} D = {2, 4, 5, 6, 7}; R = {-3, -1, 0, 2, 5} d. {(3, -4), (1, -5), (0, -2), (-2, -6), (-5, -7)}; D = {3, 1, 0, -2, -5}; R = {-7, -6, -5, -4, -2} Q6. Solve the equation 8x - 4 = 324x. a. {-12/17} b. {-4/3} c. {-2} d. {-4/17} Q7. Find the amount that results from the investment of $480 invested at 6% compounded quarterly after a period of 3 years. a. $573.90 b. $93.9 c. $565.42 d. $571.69 Q8. Solve the equation log a. {-8, -9} 72 (x2 - x) = 1. b. {1, 72} c. {8, 9} d. {-8, 9} Q9. Change the exponential expression 5-3 = 1/125 to an equivalent expression involving a logarithm. a. log -3 1/125 = 5 b. log 5 1/125 = -3 c. log 5 -3 = 1/125 d. log 1/125 5 = -3 Q10. Write log 2 (7m 3n)/k2 as the sum and/or difference of logarithms. Express powers as factors. a. (1/7) log 2 m + (1/3) log 2 n - 2log 2 k b. (1/7) log c. 7log 2 2 m (1/3) log m + 3log d. (7/2) log 2 2 2 n 2log n - 2log m + (3/2) log 2 2 2 k k n - (2/2) log Q11. Solve the equation 3(1 + 2x) = 243. 2 k a. {81} b. {2} c. {-2} d. {6} Q12. For the functions f(x) = x2 + 4 and g(x) = x2 + 1, find the composite function (f g)(x). a. x4 + 5 b. x4 + 17 c. x4 + 2x2 + 5 d. x4 + 8x2 + 17 Q13. The half-life of silicon-32 is 710 years. If 100 grams is present now, how much will be present in 200 years? (Round your answer to three decimal places.) a. 14.192 b. 82.263 c. 98.066 d. 0 Q14. Solve the equation (1/3) log a. {9} 2 (x + 6) = log 8 (3x). b. {3, 0} c. {3} d. Q15. Find the domain of the function f(x) = log 5 (100 - x2). a. (-10, 10) b. (-, -10) (10, ) c. (-100, 100) d. [-10, 10] Q16. The graph of a one-to-one function f(x) = x + 2 is given. Draw the graph of the inverse function f-1 as a dashed line or curve. a. b. Q17. In 1990, the population of a country was estimated at 4 million. For any subsequent year the population, P(t) (in millions), can be modeled by the equation P(t) = 240/(5 + 54.99e -0.0208t), where t is the number of years since 1990. Estimate the year when the population will be 21 million. a. approximately the year 2093 b. approximately the year 2041 c. approximately the year 2088 d. approximately the year 2016 Q18. Write log 7 (xy)/15 as the sum and/or difference of logarithms. Express powers as factors. a. (1/2) log 7 xy - (1/2) log 7 15 b. (1/2) log 7 x (1/2) log c. (1/2) log 7 x + (1/2) log d. (1/2) log 7 x + (1/2) log 7 y (1/2) log 7 15 7 y - (1/2) log 7 15 7 y - log 7 15 Q19. The graph of a logarithmic function is shown. Select the function which matches the graph. a. y = log 2 (x + 1) b. y = log 2 (x - 1) c. y = log 2 x d. y = log 2 x-1 Q20. Find the domain of the composite function f g if f(x) = 28/x and g(x) = -8/(x - 7). a. {x | x 7} b. {x | x 0, x 7, x 4} c. {x | x 7, x 0} d. {x | x is any real number}