What are the domain and range of mc016-1.jpg?
domain: x > 0; range: all real numbers
Which is the graph of a logarithmic function?
a Test: “Study Guide Algebra”
Which of the following is a logarithmic function?
y=log3x
What is the domain of the function?
x > -2
Which statement is true?
The graph of mc021-5.jpg is the graph of mc021-6.jpg translated 4 units up.
Which is the graph of a logarithmic function?
Which of the following is a logarithmic function?
y=log0.25x
Which statement is true?
mc009-3.jpg is not a logarithmic function because the base is equal to 1.
What is the range of mc011-1.jpg?
all real numbers
What is the solution of mc015-1.jpg?
2
What is the value of mc009-1.jpg?
2/3
A Cepheid star is a type of variable star, which means its brightness is not constant. The relationship between the brightness of a Cepheid star and its period, or length of its pulse, is given by M = -2.78(log P) - 1.35, where M is the absolute magnitude, or brightness, of the star, and P is the number of days required for the star to complete one cycle. What is the absolute magnitude of a star that has a period of 45 days? Use a calculator. Round your answer to the nearest hundredth.
-5.95
What is the value of log 43? Use the calculator. Round your answer to the nearest tenth.
1.6
The magnitude, M, of an earthquake is defined to be mc021-1.jpg, where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and S is the intensity of a "standard" earthquake, which is barely detectable. Which equation represents the magnitude of an earthquake that is 10 times more intense than a standard earthquake?
m=log 10s/s
What is the value of log 13? Use a calculator. Round your answer to the nearest tenth.
1.1
What is the value of mc005-1.jpg?
-2
Which equation has x = -6 as the solution?
log3(-2x-3)=2
Which logarithmic equation is equivalent to 82 = 64?
A.
Which logarithmic equation is equivalent to 32 = 9?
2=log3 9
Which equation is equivalent to mc010-1.jpg?
x2= 36
What is the solution of mc016-1.jpg?
4
Tyler applied the change of base formula to a logarithmic expression. The resulting expression is shown below.
mc003-1.jpg
Which expression could be Tyler's original expression?
log 12 1/4
Tenisha solved the equation below by graphing a system of equations.
mc018-1.jpg
Which point approximates the solution for Tenisha's system of equations?
(1.0, 1.4)
A teacher used the change of base formula to determine whether the equation below is correct.
mc011-1.jpg
Which statement explains whether the equation is correct?
B
What is the approximate value of q in the equation below?
mc010-1.jpg
0.585
A student solved the equation below by graphing.
mc024-1.jpg
Which statement about the graph is true?
The curves do not intersect.
What is the approximate value of x in the equation below.
mc007-1.jpg
-3.396
Kim solved the equation below by graphing a system of equations.
mc020-1.jpg
What is the approximate solution to the equation?
1.4
Which system of equations could be graphed to solve the equation below?
mc021-1.jpg
D
Omar wants to graph the system of equations below.
mc016-1.jpg
Which system of equations should Omar use?
D
Which of the following is equivalent to mc002-1.jpg?
log 1/9 -log k
Which of the following is equivalent to log9w?
log9 + logw
Given mc003-1.jpg and mc003-2.jpg, what is mc003-3.jpg?
2.402
Which expression is equivalent to mc019-1.jpg?
C
Which expression is equivalent to log3(x + 4)?
log3 + log(x + 4)
What is mc004-1.jpg written as a single log?
Logs56
The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as mc023-1.jpg, where mc023-2.jpg and is the least intense sound a human ear can hear. What is the approximate loudness of the dinner conversation, with a sound intensity of 10-7, Rajah has with his parents?
50 Db
Which expression is equivalent to mc005-1.jpg?
B
Which expression is equivalent to mc015-1.jpg?
B
Which statement is true for mc001-1.jpg
x+1=3 ^2
What is the solution to mc010-1.jpg
x = 8/3
What is the solution to mc011-1.jpg
x=2
Which of the following shows the true solution to the logarithmic equation below?
mc018-1.jpg
x= 4
Which of the following shows the extraneous solution to the logarithmic equation mc020-1.jpg
x=-4
Which of the following shows the equation mc004-1.jpg rewritten using logarithms?
C
Which of the following is true regarding the solutions to the logarithmic equation below?
x=9 is a true solution and mc015-9.jpg is an extraneous solution
What is the solution to mc005-1.jpg
x =3
Which of the following is true regarding the solutions to the logarithmic equation below?
x =6 is a true solution and mc016-7.jpg is an extraneous solution
Which of the following shows the extraneous solution(s) to the logarithmic equation?
mc021-1.jpg
x=3 and x =-7
Which of the following illustrates the product rule for logarithmic equations?
D
What is the solution to mc009-1.jpg
x=8
What is the range of the function mc021-1.jpg
all real numbers greater than 0
What is the domain of the function mc018-1.jpg graphed below?
x>0
Which equation is represented by the graph below?
y=in x
Which equation is represented by the graph below?
y=ex
What is the true solution to mc007-1.jpg
x=3
What is the true solution to mc006-1.jpg
x=2
What is the value of mc002-1.jpg
7x
Which equation is represented by the graph below?
y = In x +4
The population of a town grew from 20,000 to 28,000. The continuous growth rate is 15%. The equation mc024-1.jpg represents the situation, where t is the number of years the population has been growing. About how many years has the population of the town been growing? Use a calculator and round your answer to the nearest whole number.
2 years
What is the solution to mc013-1.jpg
x= In2 - 1
What is the value of x if mc020-1.jpg
x = In 8-6/3
What is the solution to the equation mc006-1.jpg Round your answer to the nearest hundredth.
x=0.83
What is the value of x if mc001-1.jpg
x=7
What are the potential solutions of mc015-1.jpg
x=2 and x= -8
Which equation is equivalent to mc005-1.jpg
B
What is the solution to the equation below?
mc010-1.jpg
x = 38/7
What is the value of x if mc011-1.jpg
x=5/2
What is the solution to mc003-1.jpg
x=40
What is the value of x in the equation below?
C
What is the solution to the equation below?
mc009-1.jpg
x=4
Claire deposited $2,500 into an account that accrues interest monthly. She made no additional deposits or withdrawals. After 2 years, Claire had $2,762.35 in the account. What is the annual interest rate of the account?
5%
The loudest sound measured one night during a hockey game was 112 dB. The loudest sound measured during a hockey game the next night was 118 dB. What fraction of sound intensity of the second game was the sound intensity of the first game?
0.25
Gasoline prices for the first six months of 2004 are shown in the table below. Using a logarithmic model, what is the best prediction for gas prices in the ninth month of 2004?
$2.10
The general equation for depreciation is given by y = A(1 - r)t, where y = current value, A = original cost, r = rate of depreciation, and t = time, in years. A car was purchased 6 years ago for $25,000. If the annual depreciation rate is 11%, which equation can be used to determine the approximate current value of the car?
y = 25000(0.89) ^6
The amount of a sample remaining after t days is given by the equation mc004-1.jpg, where A is the initial amount of the sample and h is the half-life, in days, of the substance. A sample contains 60% of its original amount of Fermium-257. The half-life of Fermium-257 is about 100 days. About how old is the sample?
74 days
The equation for the pH of a substance is pH = -log[H+], where H+ is the concentration of hydrogen ions. What is the approximate pH of a solution whose hydrogen ion concentration is mc015-1.jpg?
8.7
On April 11, 2012, two earthquakes were measured off the northwest coast of Sumatra. The first had a magnitude of 8.6. The second had a magnitude of 8.2. By what approximate factor was the intensity of the first earthquake greater than the intensity of the second earthquake?
2.51
The amount of a sample remaining after t days is given by the equation mc001-1.jpg, where A is the initial amount of the sample and h is the half-life, in days, of the substance. A scientist has a 10-mg sample of a radioactive isotope. The isotope has a half-life of 8 days. After 16 days, how much of the radioactive isotope remains?
2.5 mg
Jacques deposited $1,900 into an account that earns 4% interest compounded semiannually. After t years, Jacques has $3,875.79 in the account. Assuming he made no additional deposits or withdrawals, how long was the money in the account
18 years
The equation for the pH of a substance is pH = -log[H+], where H+ is the concentration of hydrogen ions. A basic solution has a pH of 11.2. An acidic solution has a pH of 2.4. What is the approximate difference in the concentration of hydrogen ions between the two solutions?
4.o x 10 -3
Over time, the number of organisms in a population increases exponentially. The table below shows the approximate number of organisms after y years.
24
