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1) Use properties of logarithms to expand the following logarithmic expression as much as possible. Logb (√xy3 / z3) A. 1/2 logb x - 6 logb y + 3 logb z B. 1/2 logb x - 9 logb y - 3 logb z C. 1/2 logb x + 3 logb y + 6 logb z D. 1/2 logb x + 3 logb y - 3 logb z 2) Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, to two decimal places, for the solution. 2 log x = log 25 A. {12} B. {5} C. {-3} D. {25} 3) Write the following equation in its equivalent logarithmic form. 2-4 = 1/16 A. Log4 1/16 = 64 B. Log2 1/24 = -4 C. Log2 1/16 = -4 D. Log4 1/16 = 54 4) Use properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. log2 96 – log2 3 A. 5 B. 7 C. 12 D. 4 5) Use the exponential growth model, A = A0ekt, to show that the time it takes a population to double (to grow from A0 to 2A0 ) is given by t = ln 2/k. A. A0 = A0ekt; ln = ekt; ln 2 = ln ekt; ln 2 = kt; ln 2/k = t B. 2A0 = A0e; 2= ekt; ln = ln ekt; ln 2 = kt; ln 2/k = t C. 2A0 = A0ekt; 2= ekt; ln 2 = ln ekt; ln 2 = kt; ln 2/k = t D. 2A0 = A0ekt; 2 = ekt; ln 1 = ln ekt; ln 2 = kt; ln 2/k = toe 6) Find the domain of following logarithmic function. f(x) = log (2 - x) A. (∞, 4) B. (∞, -12) C. (-∞, 2) D. (-∞, -3) 7) An artifact originally had 16 grams of carbon-14 present. The decay model A = 16e -0.000121t describes the amount of carbon-14 present after t years. How many grams of carbon-14 will be present in 5715 years? A. Approximately 7 grams B. Approximately 8 grams C. Approximately 23 grams D. Approximately 4 grams 8) Use properties of logarithms to expand the following logarithmic expression as much as possible. logb (x2 y) / z2 A. 2 logb x + logb y - 2 logb z B. 4 logb x - logb y - 2 logb z C. 2 logb x + 2 logb y + 2 logb z D. logb x - logb y + 2 logb z 9) The exponential function f with base b is defined by f(x) = __________, b > 0 and b ≠ 1. Using interval notation, the domain of this function is __________ and the range is __________. A. bx; (∞, -∞); (1, ∞) B. bx; (-∞, -∞); (2, ∞) C. bx; (-∞, ∞); (0, ∞) D. bx; (-∞, -∞); (-1, ∞) 10) Approximate the following using a calculator; round your answer to three decimal places. 3√5 A. .765 B. 14297 C. 11.494 D. 11.665 11) Write the following equation in its equivalent exponential form. 4 = log2 16 A. 2 log4 = 16 B. 22 = 4 C. 44 = 256 D. 24 = 16 12) Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents. 31-x = 1/27 A. {2} B. {-7} C. {4} D. {3} 13) Use properties of logarithms to expand the following logarithmic expression as much as possible. logb (x2y) A. 2 logy x + logx y B. 2 logb x + logb y C. logx - logb y D. logb x – ...
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