Algebra 2b – Flashcards
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What are the domain and range of mc016-1.jpg?
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domain: x > 0; range: all real numbers
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Which is the graph of a logarithmic function?
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a Test: “Study Guide Algebra”
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Which of the following is a logarithmic function?
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y=log3x
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What is the domain of the function?
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x > -2
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Which statement is true?
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The graph of mc021-5.jpg is the graph of mc021-6.jpg translated 4 units up.
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Which of the following is a logarithmic function?
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y=log0.25x
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Which statement is true?
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mc009-3.jpg is not a logarithmic function because the base is equal to 1.
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What is the range of mc011-1.jpg?
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all real numbers
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What is the solution of mc015-1.jpg?
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2
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What is the value of mc009-1.jpg?
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2/3
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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.
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-5.95
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What is the value of log 43? Use the calculator. Round your answer to the nearest tenth.
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1.6
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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?
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m=log 10s/s
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What is the value of log 13? Use a calculator. Round your answer to the nearest tenth.
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1.1
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What is the value of mc005-1.jpg?
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-2
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Which equation has x = -6 as the solution?
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log3(-2x-3)=2
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Which logarithmic equation is equivalent to 82 = 64?
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A.
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Which logarithmic equation is equivalent to 32 = 9?
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2=log3 9
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Which equation is equivalent to mc010-1.jpg?
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x2= 36
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What is the solution of mc016-1.jpg?
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4
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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?
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log 12 1/4
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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?
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(1.0, 1.4)
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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?
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B
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What is the approximate value of q in the equation below? mc010-1.jpg
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0.585
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A student solved the equation below by graphing. mc024-1.jpg Which statement about the graph is true?
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The curves do not intersect.
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What is the approximate value of x in the equation below. mc007-1.jpg
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-3.396
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Kim solved the equation below by graphing a system of equations. mc020-1.jpg What is the approximate solution to the equation?
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1.4
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Which system of equations could be graphed to solve the equation below? mc021-1.jpg
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D
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Omar wants to graph the system of equations below. mc016-1.jpg Which system of equations should Omar use?
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D
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Which of the following is equivalent to mc002-1.jpg?
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log 1/9 -log k
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Which of the following is equivalent to log9w?
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log9 + logw
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Given mc003-1.jpg and mc003-2.jpg, what is mc003-3.jpg?
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2.402
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Which expression is equivalent to mc019-1.jpg?
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C
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Which expression is equivalent to log3(x + 4)?
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log3 + log(x + 4)
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What is mc004-1.jpg written as a single log?
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Logs56
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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?
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50 Db
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Which expression is equivalent to mc005-1.jpg?
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B
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Which expression is equivalent to mc015-1.jpg?
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B
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Which statement is true for mc001-1.jpg
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x+1=3 ^2
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What is the solution to mc010-1.jpg
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x = 8/3
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What is the solution to mc011-1.jpg
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x=2
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Which of the following shows the true solution to the logarithmic equation below? mc018-1.jpg
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x= 4
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Which of the following shows the extraneous solution to the logarithmic equation mc020-1.jpg
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x=-4
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Which of the following shows the equation mc004-1.jpg rewritten using logarithms?
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C
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Which of the following is true regarding the solutions to the logarithmic equation below?
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x=9 is a true solution and mc015-9.jpg is an extraneous solution
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What is the solution to mc005-1.jpg
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x =3
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Which of the following is true regarding the solutions to the logarithmic equation below?
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x =6 is a true solution and mc016-7.jpg is an extraneous solution
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Which of the following shows the extraneous solution(s) to the logarithmic equation? mc021-1.jpg
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x=3 and x =-7
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Which of the following illustrates the product rule for logarithmic equations?
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D
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What is the solution to mc009-1.jpg
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x=8
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What is the range of the function mc021-1.jpg
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all real numbers greater than 0
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What is the domain of the function mc018-1.jpg graphed below?
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x>0
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Which equation is represented by the graph below?
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y=in x
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Which equation is represented by the graph below?
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y=ex
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What is the true solution to mc007-1.jpg
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x=3
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What is the true solution to mc006-1.jpg
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x=2
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What is the value of mc002-1.jpg
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7x
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Which equation is represented by the graph below?
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y = In x +4
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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.
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2 years
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What is the solution to mc013-1.jpg
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x= In2 - 1
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What is the value of x if mc020-1.jpg
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x = In 8-6/3
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What is the solution to the equation mc006-1.jpg Round your answer to the nearest hundredth.
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x=0.83
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What is the value of x if mc001-1.jpg
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x=7
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What are the potential solutions of mc015-1.jpg
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x=2 and x= -8
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Which equation is equivalent to mc005-1.jpg
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B
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What is the solution to the equation below? mc010-1.jpg
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x = 38/7
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What is the value of x if mc011-1.jpg
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x=5/2
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What is the solution to mc003-1.jpg
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x=40
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What is the value of x in the equation below?
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C
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What is the solution to the equation below? mc009-1.jpg
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x=4
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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?
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5%
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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?
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0.25
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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?
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$2.10
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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?
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y = 25000(0.89) ^6
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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?
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74 days
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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?
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8.7
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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?
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2.51
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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?
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2.5 mg
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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
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18 years
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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?
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4.o x 10 -3
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Over time, the number of organisms in a population increases exponentially. The table below shows the approximate number of organisms after y years.
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24
