Question 1 of 40
5.0 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 2 of 40
5.0 Points
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
Question 3 of 40
5.0 Points
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
Question 4 of 40
5.0 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 5 of 40
5.0 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 6 of 40
5.0 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 7 of 40
5.0 Points
Evaluate the following expression without using a calculator.
8log8 19
• A. 17
• B. 38
• C. 24
• D. 19
Question 8 of 40
5.0 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 9 of 40
5.0 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?
Question 10 of 40
5.0 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 11 of 40
5.0 Points
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?
Question 12 of 40
5.0 Points
Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents.
31-x = 1/27
Question 13 of 40
5.0 Points
Find the domain of following logarithmic function.
f(x) = ln (x - 2)2
Question 14 of 40
5.0 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.
Question 15 of 40
5.0 Points
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.
Question 16 of 40
5.0 Points
Find the domain of following logarithmic function.
f(x) = log (2 - x)
Question 17 of 40
5.0 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.
Question 18 of 40
5.0 Points
Write the following equation in its equivalent exponential form.
log6 216 = y
Question 19 of 40
5.0 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
Question 20 of 40
5.0 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
Question 21 of 40
5.0 Points
Let x represent one number and let y represent the other number. Use the given conditions to write a system of equations. Solve the system and find the numbers.
The sum of two numbers is 7. If one number is subtracted from the other, their difference is -1. Find the numbers.
Question 22 of 40
5.0 Points
Solve each equation by either substitution or addition method.
x2 + 4y2 = 20
x + 2y = 6
Question 23 of 40
5.0 Points
Solve each equation by the substitution method.
x + y = 1
x2 + xy – y2 = -5
Question 24 of 40
5.0 Points
Solve each equation by the substitution method.
x2 - 4y2 = -7
3x2 + y2 = 31
Question 25 of 40
5.0 Points
Perform the long division and write the partial fraction decomposition of the remainder term.
x4 – x2 + 2/x3 - x2
Question 26 of 40
5.0 Points
Solve the following system.
2x + 4y + 3z = 2
x + 2y - z = 0
4x + y - z = 6
Question 27 of 40
5.0 Points
Write the partial fraction decomposition for the following rational expression.
x2 – 6x + 3/(x – 2)3
Question 28 of 40
5.0 Points
Write the partial fraction decomposition for the following rational expression.
x + 4/x2(x + 4)
Question 29 of 40
5.0 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.
Question 30 of 40
5.0 Points
A television manufacturer makes rear-projection and plasma televisions. The profit per unit is $125 for the rear-projection televisions and $200 for the plasma televisions.
Let x = the number of rear-projection televisions manufactured in a month and let y = the number of plasma televisions manufactured in a month. Write the objective function that models the total monthly profit.
Question 31 of 40
5.0 Points
Write the form of the partial fraction decomposition of the rational expression.
7x - 4/x2 - x - 12
Question 32 of 40
5.0 Points
Find the quadratic function y = ax2 + bx + c whose graph passes through the given points.
(-1, 6), (1, 4), (2, 9)
Question 33 of 40
5.0 Points
Solve each equation by the addition method.
x2 + y2 = 25
(x - 8)2 + y2 = 41
Question 34 of 40
5.0 Points
Perform the long division and write the partial fraction decomposition of the remainder term.
x5 + 2/x2 - 1
Question 35 of 40
5.0 Points
Write the partial fraction decomposition for the following rational expression.
ax +b/(x – c)2 (c ≠ 0)
Question 36 of 40
5.0 Points
Find the quadratic function y = ax2 + bx + c whose graph passes through the given points.
(-1, -4), (1, -2), (2, 5)
Question 37 of 40
5.0 Points
Solve the following system by the substitution method.
{x + y = 4
{y = 3x
Question 38 of 40
5.0 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.
Question 39 of 40
5.0 Points
Solve the following system by the substitution method.
{x + 3y = 8
{y = 2x - 9
Question 40 of 40
5.0 Points
Solve the following system.
x = y + 4
3x + 7y = -18
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