Use properties of logarithms to condense the following logarithmic expression….

Question 1 of 400.0/ 2.5 PointsUse properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1.3 ln x – 1/3 ln yA. ln (x / y1/2)B. lnx (x6 / y1/3)C. ln (x3/ y1/3)D. ln (x-3 / y1/4)Question 2 of 402.5/ 2.5 PointsThe 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, ?)Question 3 of 402.5/ 2.5 PointsUse properties of logarithms to expand the following logarithmic expression as much as possible.logb (x2y)A. 2 logyx + logxyB. 2 logbx + logbyC. logx – logbyD. logbx – logxyQuestion 4 of 402.5/ 2.5 PointsSolve the following exponential equation. Express the solution set in terms of natural logarithms or common logarithms to a decimal approximation, of two decimal places, for the solution.32x + 3x – 2 = 0A. {1}B. {-2}C. {5}D. {0}Question 5 of 402.5/ 2.5 PointsUse properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1.log x + 3 log yA. log (xy)B. log (xy3)C. log (xy2)D. logy (xy)3Question 6 of 400.0/ 2.5 PointsWrite the following equation in its equivalent exponential form.5 = logb 32A. b5 = 32B. y5 = 32C. Blog5 = 32D. Logb = 32Question 7 of 402.5/ 2.5 PointsUse properties of logarithms to expand the following logarithmic expression as much as possible.logb (x2 y) / z2A. 2 logb x + logb y – 2 logb zB. 4 logb x – logb y – 2 logb zC. 2 logb x + 2 logb y + 2 logb zD. logb x – logb y + 2 logb zQuestion 8 of 400.0/ 2.5 PointsConsider the model for exponential growth or decay given by A = A0ekt. If k __________, the function models the amount, or size, of a growing entity. If k __________, the function models the amount, or size, of a decaying entity.A. > 0; < 0B. = 0; ? 0C. ? 0; < 0D. < 0; ? 0Question 9 of 402.5/ 2.5 PointsEvaluate the following expression without using a calculator.Log7 ?7A. 1/4B. 3/5C. 1/2D. 2/7Question 10 of 402.5/ 2.5 PointsThe half-life of the radioactive element krypton-91 is 10 seconds. If 16 grams of krypton-91 are initially present, how many grams are present after 10 seconds? 20 seconds?A. 10 grams after 10 seconds; 6 grams after 20 secondsB. 12 grams after 10 seconds; 7 grams after 20 secondsC. 4 grams after 10 seconds; 1 gram after 20 secondsD. 8 grams after 10 seconds; 4 grams after 20 secondsQuestion 11 of 400.0/ 2.5 PointsWrite the following equation in its equivalent exponential form.4 = log2 16A. 2 log4 = 16B. 22 = 4C. 44 = 256D. 24 = 16Question 12 of 402.5/ 2.5 PointsSolve 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 25A. {12}B. {5}C. {-3}D. {25}Question 13 of 402.5/ 2.5 PointsFind the domain of following logarithmic function.f(x) = log5 (x + 4)A. (-4, ?)B. (-5, -?)C. (7, -?)D. (-9, ?)Question 14 of 400.0/ 2.5 PointsApproximate the following using a calculator; round your answer to three decimal places.3?5A. .765B. 14297C. 11.494D. 11.665Question 15 of 400.0/ 2.5 PointsThe graph of the exponential function f with base b approaches, but does not touch, the __________-axis. This axis, whose equation is __________, is a __________ asymptote.A. x; y = 0; horizontalB. x; y = 1; verticalC. -x; y = 0; horizontalD. x; y = -1; verticalQuestion 16 of 400.0/ 2.5 PointsFind the domain of following logarithmic function.f(x) = ln (x - 2)2A. (?, 2) ? (-2, -?)B. (-?, 2) ? (2, ?)C. (-?, 1) ? (3, ?)D. (2, -?) ? (2, ?)Question 17 of 402.5/ 2.5 PointsApproximate the following using a calculator; round your answer to three decimal places.e-0.95A. .483B. 1.287C. .597D. .387Question 18 of 400.0/ 2.5 PointsUse properties of logarithms to expand the following logarithmic expression as much as possible.Logb (?xy3/ z3)A. 1/2 logbx - 6 logby + 3 logbzB. 1/2 logb x - 9 logb y - 3 logb zC. 1/2 logb x + 3 logb y + 6 logb zD. 1/2 logb x + 3 logb y - 3 logb zQuestion 19 of 402.5/ 2.5 PointsYou have $10,000 to invest. One bank pays 5% interest compounded quarterly and a second bank pays 4.5% interest compounded monthly. Use the formula for compound interest to write a function for the balance in each bank at any time t.A. A = 20,000(1 + (0.06/4))4t; A = 10,000(1 + (0.044/14))12tB. A = 15,000(1 + (0.07/4))4t; A = 10,000(1 + (0.025/12))12tC. A = 10,000(1 + (0.05/4))4t; A = 10,000(1 + (0.045/12))12tD. A = 25,000(1 + (0.05/4))4t; A = 10,000(1 + (0.032/14))12tQuestion 20 of 402.5/ 2.5 PointsWrite the following equation in its equivalent exponential form.log6 216 = yA. 6y = 216B. 6x = 216C. 6logy = 224D. 6xy = 232Part 2 of 2 - Lesson 5 Questions10.0/ 50.0 PointsQuestion 21 of 400.0/ 2.5 PointsWrite the form of the partial fraction decomposition of the rational expression. 7x - 4/x2 - x - 12A. 24/7(x - 2) + 26/7(x + 5)B. 14/7(x - 3) + 20/7(x2 + 3)C. 24/7(x - 4) + 25/7(x + 3)D. 22/8(x - 2) + 25/6(x + 4)Question 22 of 400.0/ 2.5 PointsSolve each equation by the addition method.x2 + y2 = 25 (x - 8)2 + y2 = 41A. {(3, 5), (3, -2)}B. {(3, 4), (3, -4)}C. {(2, 4), (1, -4)}D. {(3, 6), (3, -7)}Question 23 of 400.0/ 2.5 PointsFind the quadratic function y = ax2 + bx + c whose graph passes through the given points.(-1, 6), (1, 4), (2, 9)A. y = 2x2 - x + 3B. y = 2x2 + x2 + 9C. y = 3x2 - x - 4D. y = 2x2 + 2x + 4Question 24 of 400.0/ 2.5 PointsSolve the following system by the substitution method.{x + y = 4 {y = 3xA. {(1, 4)}B. {(3, 3)}C. {(1, 3)}D. {(6, 1)}Question 25 of 400.0/ 2.5 PointsSolve the following system.x + y + z = 6 3x + 4y - 7z = 1 2x - y + 3z = 5A. {(1, 3, 2)}B. {(1, 4, 5)}C. {(1, 2, 1)}D. {(1, 5, 7)}Question 26 of 402.5/ 2.5 PointsSolve the following system.x = y + 4 3x + 7y = -18A. {(2, -1)}B. {(1, 4)}C. {(2, -5)}D. {(1, -3)}Question 27 of 400.0/ 2.5 PointsSolve the following system by the substitution method.{x + 3y = 8 {y = 2x - 9A. {(5, 1)}B. {(4, 3)}C. {(7, 2)}D. {(4, 3)}Question 28 of 400.0/ 2.5 PointsSolve each equation by either substitution or addition method.x2 + 4y2 = 20 x + 2y = 6A. {(5, 2), (-4, 1)}B. {(4, 2), (3, 1)}C. {(2, 2), (4, 1)}D. {(6, 2), (7, 1)}Question 29 of 400.0/ 2.5 PointsFind the quadratic function y = ax2 + bx + c whose graph passes through the given points.(-1, -4), (1, -2), (2, 5)A. y = 2x2 + x - 6B. y = 2x2 + 2x - 4C. y = 2x2 + 2x + 3D. y = 2x2 + x - 5Question 30 of 400.0/ 2.5 PointsWrite the partial fraction decomposition for the following rational expression.x + 4/x2(x + 4)A. 1/3x + 1/x2 - x + 5/4(x2 + 4)B. 1/5x + 1/x2 - x + 4/4(x2 + 6)C. 1/4x + 1/x2 - x + 4/4(x2 + 4)D. 1/3x + 1/x2 - x + 3/4(x2 + 5)Question 31 of 400.0/ 2.5 PointsSolve the following system by the addition method.{2x + 3y = 6 {2x – 3y = 6A. {(4, 1)}B. {(5, 0)}C. {(2, 1)}D. {(3, 0)}Question 32 of 402.5/ 2.5 PointsWrite the partial fraction decomposition for the following rational expression.1/x2 – c2 (c ? 0)A. 1/4c/x - c - 1/2c/x + cB. 1/2c/x - c - 1/2c/x + cC. 1/3c/x - c - 1/2c/x + cD. 1/2c/x - c - 1/3c/x + cQuestion 33 of 400.0/ 2.5 PointsPerform the long division and write the partial fraction decomposition of the remainder term.x5 + 2/x2 - 1A. x2 + x - 1/2(x + 1) + 4/2(x - 1)B. x3 + x - 1/2(x + 1) + 3/2(x - 1)C. x3 + x - 1/6(x - 2) + 3/2(x + 1)D. x2 + x - 1/2(x + 1) + 4/2(x - 1)Question 34 of 400.0/ 2.5 PointsWrite the partial fraction decomposition for the following rational expression.x2 – 6x + 3/(x – 2)3A. 1/x – 4 – 2/(x – 2)2 – 6/(x – 2)B. 1/x – 2 – 4/(x – 2)2 – 5/(x – 1)3C. 1/x – 3 – 2/(x – 3)2 – 5/(x – 2)D. 1/x – 2 – 2/(x – 2)2 – 5/(x – 2)3Question 35 of 402.5/ 2.5 PointsOn your next vacation, you will divide lodging between large resorts and small inns. Let x represent the number of nights spent in large resorts. Let y represent the number of nights spent in small inns.Write a system of inequalities that models the following conditions:You want to stay at least 5 nights. At least one night should be spent at a large resort. Large resorts average $200 per night and small inns average $100 per night. Your budget permits no more than $700 for lodging.A.y ? 1 x + y ? 5x ? 1 300x + 200y ? 700B.y ? 0x + y ? 3 x ? 0 200x + 200y ? 700C.y ? 1x + y ? 4x ? 2 500x + 100y ? 700D.y ? 0x + y ? 5x ? 1 200x + 100y ? 700Question 36 of 400.0/ 2.5 PointsSolve each equation by the substitution method.y2 = x2 - 9 2y = x – 3A. {(-6, -4), (2, 0)}B. {(-4, -4), (1, 0)}C. {(-3, -4), (2, 0)}D. {(-5, -4), (3, 0)}Question 37 of 400.0/ 2.5 PointsPerform the long division and write the partial fraction decomposition of the remainder term.x4 – x2 + 2/x3 - x2A. x + 3 - 2/x - 1/x2 + 4x - 1B. 2x + 1 - 2/x - 2/x + 2/x + 1C. 2x + 1 - 2/x2 - 2/x + 5/x - 1D. x + 1 - 2/x - 2/x2 + 2/x - 1Question 38 of 400.0/ 2.5 PointsWrite the partial fraction decomposition for the following rational expression.6x - 11/(x - 1)2A. 6/x - 1 - 5/(x - 1)2B. 5/x - 1 - 4/(x - 1)2C. 2/x - 1 - 7/(x - 1)D. 4/x - 1 - 3/(x - 1)Question 39 of 402.5/ 2.5 PointsMany elevators have a capacity of 2000 pounds.If a child averages 50 pounds and an adult 150 pounds, write an inequality that describes when x children and y adults will cause the elevator to be overloaded.A. 50x + 150y > 2000B. 100x + 150y > 1000C. 70x + 250y > 2000D. 55x + 150y > 3000Question 40 of 400.0/ 2.5 PointsSolve each equation by the substitution method.x2 – 4y2 = -7 3×2 + y2 = 31A. {(2, 2), (3, -2), (-1, 2), (-4, -2)}B. {(7, 2), (3, -2), (-4, 2), (-3, -1)}C. {(4, 2), (3, -2), (-5, 2), (-2, -2)}D. {(3, 2), (3, -2), (-3, 2), (-3, -2)}