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

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

Question # 00041755 Posted By: jia_andy Updated on: 01/15/2015 10:34 AM Due on: 02/15/2015
Subject Mathematics Topic General Mathematics Tutorials:
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Question 1 of 40



0.0/ 2.5 Points



Use 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 y


















A. ln (x / y1/2)



B. lnx (x6 / y1/3)



C. ln (x3/ y1/3)



D. ln (x-3 / y1/4)












Question 2 of 40



2.5/ 2.5 Points



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, ?)












Question 3 of 40



2.5/ 2.5 Points



Use properties of logarithms to expand the following logarithmic expression as much as possible.

logb (x2y)


















A. 2 logyx + logxy



B. 2 logbx + logby



C. logx - logby



D. logbx – logxy












Question 4 of 40



2.5/ 2.5 Points



Solve 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 = 0


















A. {1}



B. {-2}



C. {5}



D. {0}












Question 5 of 40



2.5/ 2.5 Points



Use properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1.

log x + 3 log y


















A. log (xy)



B. log (xy3)



C. log (xy2)



D. logy (xy)3












Question 6 of 40



0.0/ 2.5 Points



Write the following equation in its equivalent exponential form.

5 = logb 32


















A. b5 = 32



B. y5 = 32



C. Blog5 = 32



D. Logb = 32












Question 7 of 40



2.5/ 2.5 Points



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












Question 8 of 40



0.0/ 2.5 Points



Consider 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; < 0



B. = 0; ? 0



C. ? 0; < 0



D. < 0; ? 0












Question 9 of 40



2.5/ 2.5 Points



Evaluate the following expression without using a calculator.

Log7 ?7


















A. 1/4



B. 3/5



C. 1/2



D. 2/7












Question 10 of 40



2.5/ 2.5 Points



The 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 seconds



B. 12 grams after 10 seconds; 7 grams after 20 seconds



C. 4 grams after 10 seconds; 1 gram after 20 seconds



D. 8 grams after 10 seconds; 4 grams after 20 seconds












Question 11 of 40



0.0/ 2.5 Points



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












Question 12 of 40



2.5/ 2.5 Points



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}












Question 13 of 40



2.5/ 2.5 Points



Find the domain of following logarithmic function.

f(x) = log5 (x + 4)


















A. (-4, ?)



B. (-5, -?)



C. (7, -?)



D. (-9, ?)












Question 14 of 40



0.0/ 2.5 Points



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












Question 15 of 40



0.0/ 2.5 Points



The 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; horizontal



B. x; y = 1; vertical



C. -x; y = 0; horizontal



D. x; y = -1; vertical












Question 16 of 40



0.0/ 2.5 Points



Find the domain of following logarithmic function.

f(x) = ln (x - 2)2


















A. (?, 2) ? (-2, -?)



B. (-?, 2) ? (2, ?)



C. (-?, 1) ? (3, ?)



D. (2, -?) ? (2, ?)












Question 17 of 40



2.5/ 2.5 Points



Approximate the following using a calculator; round your answer to three decimal places.

e-0.95


















A. .483



B. 1.287



C. .597



D. .387












Question 18 of 40



0.0/ 2.5 Points



Use properties of logarithms to expand the following logarithmic expression as much as possible.

Logb (?xy3/ z3)


















A. 1/2 logbx - 6 logby + 3 logbz



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












Question 19 of 40



2.5/ 2.5 Points



You 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))12t



B. A = 15,000(1 + (0.07/4))4t; A = 10,000(1 + (0.025/12))12t



C. A = 10,000(1 + (0.05/4))4t; A = 10,000(1 + (0.045/12))12t



D. A = 25,000(1 + (0.05/4))4t; A = 10,000(1 + (0.032/14))12t












Question 20 of 40



2.5/ 2.5 Points



Write the following equation in its equivalent exponential form.

log6 216 = y


















A. 6y = 216



B. 6x = 216



C. 6logy = 224



D. 6xy = 232













Part 2 of 2 - Lesson 5 Questions



10.0/ 50.0 Points











































































Question 21 of 40



0.0/ 2.5 Points



Write the form of the partial fraction decomposition of the rational expression.
7x - 4/x2 - x - 12


















A. 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 40



0.0/ 2.5 Points



Solve each equation by the addition method.









x2 + y2 = 25
(x - 8)2 + y2 = 41



















A. {(3, 5), (3, -2)}



B. {(3, 4), (3, -4)}



C. {(2, 4), (1, -4)}



D. {(3, 6), (3, -7)}












Question 23 of 40



0.0/ 2.5 Points



Find the quadratic function y = ax2 + bx + c whose graph passes through the given points.

(-1, 6), (1, 4), (2, 9)


















A. y = 2x2 - x + 3



B. y = 2x2 + x2 + 9



C. y = 3x2 - x - 4



D. y = 2x2 + 2x + 4












Question 24 of 40



0.0/ 2.5 Points



Solve the following system by the substitution method.

{x + y = 4
{y = 3x


















A. {(1, 4)}



B. {(3, 3)}



C. {(1, 3)}



D. {(6, 1)}












Question 25 of 40



0.0/ 2.5 Points



Solve the following system.









x + y + z = 6
3x + 4y - 7z = 1
2x - y + 3z = 5



















A. {(1, 3, 2)}



B. {(1, 4, 5)}



C. {(1, 2, 1)}



D. {(1, 5, 7)}












Question 26 of 40



2.5/ 2.5 Points



Solve the following system.









x = y + 4
3x + 7y = -18



















A. {(2, -1)}



B. {(1, 4)}



C. {(2, -5)}



D. {(1, -3)}












Question 27 of 40



0.0/ 2.5 Points



Solve the following system by the substitution method.

{x + 3y = 8
{y = 2x - 9


















A. {(5, 1)}



B. {(4, 3)}



C. {(7, 2)}



D. {(4, 3)}












Question 28 of 40



0.0/ 2.5 Points



Solve each equation by either substitution or addition method.









x2 + 4y2 = 20
x + 2y = 6



















A. {(5, 2), (-4, 1)}



B. {(4, 2), (3, 1)}



C. {(2, 2), (4, 1)}



D. {(6, 2), (7, 1)}












Question 29 of 40



0.0/ 2.5 Points



Find the quadratic function y = ax2 + bx + c whose graph passes through the given points.

(-1, -4), (1, -2), (2, 5)


















A. y = 2x2 + x - 6



B. y = 2x2 + 2x - 4



C. y = 2x2 + 2x + 3



D. y = 2x2 + x - 5












Question 30 of 40



0.0/ 2.5 Points



Write 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 40



0.0/ 2.5 Points



Solve the following system by the addition method.

{2x + 3y = 6
{2x – 3y = 6


















A. {(4, 1)}



B. {(5, 0)}



C. {(2, 1)}



D. {(3, 0)}












Question 32 of 40



2.5/ 2.5 Points



Write the partial fraction decomposition for the following rational expression.

1/x2 – c2 (c ? 0)


















A. 1/4c/x - c - 1/2c/x + c



B. 1/2c/x - c - 1/2c/x + c



C. 1/3c/x - c - 1/2c/x + c



D. 1/2c/x - c - 1/3c/x + c












Question 33 of 40



0.0/ 2.5 Points



Perform the long division and write the partial fraction decomposition of the remainder term.

x5 + 2/x2 - 1


















A. 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 40



0.0/ 2.5 Points



Write the partial fraction decomposition for the following rational expression.

x2 – 6x + 3/(x – 2)3


















A. 1/x – 4 – 2/(x – 2)2 – 6/(x – 2)



B. 1/x – 2 – 4/(x – 2)2 – 5/(x – 1)3



C. 1/x – 3 – 2/(x – 3)2 – 5/(x – 2)



D. 1/x – 2 – 2/(x – 2)2 – 5/(x – 2)3












Question 35 of 40



2.5/ 2.5 Points



On 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 ? 5
x ? 1
300x + 200y ? 700




B.









y ? 0
x + y ? 3
x ? 0
200x + 200y ? 700




C.









y ? 1
x + y ? 4
x ? 2
500x + 100y ? 700




D.









y ? 0
x + y ? 5
x ? 1
200x + 100y ? 700













Question 36 of 40



0.0/ 2.5 Points



Solve each equation by the substitution method.









y2 = x2 - 9
2y = x – 3



















A. {(-6, -4), (2, 0)}



B. {(-4, -4), (1, 0)}



C. {(-3, -4), (2, 0)}



D. {(-5, -4), (3, 0)}












Question 37 of 40



0.0/ 2.5 Points



Perform the long division and write the partial fraction decomposition of the remainder term.

x4 – x2 + 2/x3 - x2


















A. x + 3 - 2/x - 1/x2 + 4x - 1



B. 2x + 1 - 2/x - 2/x + 2/x + 1



C. 2x + 1 - 2/x2 - 2/x + 5/x - 1



D. x + 1 - 2/x - 2/x2 + 2/x - 1












Question 38 of 40



0.0/ 2.5 Points



Write the partial fraction decomposition for the following rational expression.

6x - 11/(x - 1)2


















A. 6/x - 1 - 5/(x - 1)2



B. 5/x - 1 - 4/(x - 1)2



C. 2/x - 1 - 7/(x - 1)



D. 4/x - 1 - 3/(x - 1)












Question 39 of 40



2.5/ 2.5 Points



Many 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 > 2000



B. 100x + 150y > 1000



C. 70x + 250y > 2000



D. 55x + 150y > 3000












Question 40 of 40



0.0/ 2.5 Points



Solve each equation by the substitution method.









x2 - 4y2 = -7
3x2 + y2 = 31



















A. {(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)}



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