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

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 logy x + logx y

B. 2 logb x + logb y

C. logx - logb y

D. logb x – logx y

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 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

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.

y ≥ 1
x + y ≥ 5
x ≥ 1
300x + 200y ≤ 700

y ≥ 0
x + y ≥ 3
x ≥ 0
200x + 200y ≤ 700

y ≥ 1
x + y ≥ 4
x ≥ 2
500x + 100y ≤ 700

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

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