Algebra 3

Approximate: log 5 4/7

( B ) -0.3477

Approximate: log 1/2 5

( C ) -2.3219

The expression mc001-1.jpg is the result of applying the change of base formula to a logarithmic expression. Which could be the original expression?

( C ) log 2 1/3

Which expression is equivalent to 6^-3

(1/6)^3

Which of the following describes the transformations of mc020-1.jpg from the parent function mc020-2.jpg?

(A) shift 4 units left, reflect over the x-axis, shift 2 units down

what are the domain and range of f(x)=(1/5)^x

(B) The domain is all real numbers. The range is all real numbers greater than zero.

Which set of ordered pairs could be generated by an exponential function?

(D) (0, 1), (1, 3), (2, 9), (3, 27)

Solve log2(x - 1) = log12(x - 1) by graphing. x =

2

Solve log2x = log53 + 1 by graphing. Round to the nearest tenth.

3.2

Evaluate log12y2, given log12y = 16.

32

Which is equivalent to 3log28 + 4log212 − log32?

5-log3(2)

The pH of a particular solution is given by pH = -log(x-2) , where x represents the concentration of the hydrogen ions in the solution, in moles per liter. Which graph models the pH of this solution?

A

What is the approximate value of x in the equation below. log3/425 = 3x-1

A

Which expression can be used to approximate the expression below, for all positive numbers a, b, and x, where a ≠ 1 and b ≠ 1? logax

A

Which table represents the graph of a logarithmic function in the form y = logbX when b > 1

A

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?

A $2.10

Which graph represents an exponential function?

A (l-shaped)

For what value of a does 9 = (1/27)^a+3

A -11/3

For what value of a does (1/9)^a+1 = 81^a+1 * 27^2-a

A -4

A student solved the equation below by graphing. log6(x-1) = log2(2x+2) Which statement about the graph is true?

A The curves do not intersect.

Which of the following is equivalent to log9w?

A log9 + logw

The atmospheric pressure at sea level is 14.7 lb/in^2. This pressure is reduced by half for each 3.6 miles above sea level. Which graph correctly identifies the amount of atmospheric pressure based on height, in miles, above sea level?

B

Tyler applied the change of base formula to a logarithmic expression. The resulting expression is shown below. log 1/4 / log12 Which expression could be Tyler's original expression?

B

What are the domain and range of the function f(x) = 3x + 5?

B

Which graph shows the solution to the equation log2(3x - 1) = 2?

B

Which of the following shows the graph of y = -(2)x - 1?

B

Which point corresponds to the real zero of the graph of y = log3(x+2) - 1?

B (1,0)

Tenisha solved the equation below by graphing a system of equations. log3^5x = log5(2x+8) Which point approximates the solution for Tenisha's system of equations?

B (1.0 , 1.4)

The table shows a student's proof of the quotient rule for logarithms. Let M = b^x and N = b^y for some real numbers x and y. What is the error in the proof?

B The error is in step 3. You cannot use a property of logarithms to prove that the same property.

What are the domain and range of f(x) = log(x+6)-4

B domain: x > -6; range: all real numbers

Which expression is equivalent to log12((1/2)/8w)?

B log12^1/2-(log12^8+log12^W)

For what values of x does

B. x=-3, x=1

Food poisoning occurs when bacteria like Salmonella and Listeria grow on food. These microorganisms grow at an exponential rate. When an initial population of 100 bacteria are left at 98.6 degrees F, they will grow at a rate of b = 100(8)^h. Which graph could be used to calculate the number of bacteria after a certain number of hours?

C

Which of the following shows the graph of y = 2e^x?

C

Which set of ordered pairs could be generated by a

C

Which set of ordered pairs could be generated by an exponential function

C (1,1/2) , (2,1/4) , (3,1/8) , (4,1/16)

Which of the following is equivalent to (1/2)^-2t?

C (2^2)^t

What is the approximate value of q in the equation below? q + log2^6 = 2q + 2

C 0.585

Which of the following is true regarding the solutions to the logarithmic equation below? 2log6(x) = 2 log6(x^2) = 2 x^2 = 6^2 x^2 = 36 x = 6 , -6

C x = 6 is a true solution and x = -6 is an extraneous solution

What is the value of x in the equation below? 1 + 2e^x+1 = 9

C x = ln4 - 1

Which of the following exponential equations could be represented by the table below?

C y = 3^x-3 + 2

Which equation is represented by the graph below?

C y = e^x

Which equation is represented by the graph below?

C y = ln x+4

Which of the following is a logarithmic function?

C y = log0.25X

Which statement is true

C y = log1X is not a logarithmic function because the base is equal to 1

Which expression is equivalent to (10x)^-3

C 1/1000x^3

Which function has a range of y < 3

C y = -(2)^x + 3

An equation for the depreciation of a car is given by y = A(1 - r)t, where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The current value of a car is $12,282.50. The car originally cost $20,000 and depreciates at a rate of 15% per year. How old is the car?

C. 3 years

For what value of y does 125 = (1/25)^y-1

D -1/2

Consider the expression 1.1(1.3)^x+4. Which of the following is an equivalent expression?

D 1.1(1.3)^4(1.3)^x

Describe how to simplify the expression 3^-6/3^-4

Keep the base the same and then subtract the exponents

Benford's law states that the probability that a number in a set has a given leading digit, d, isP(d) = log(d + 1) - log(d).State which property you would use to rewrite the expression as a single logarithm, and rewrite the logarithm. What is the probability that the number 1 is the leading digit? Explain.

Use the quotient property to rewrite the expression. Write the difference of logs as the quotient log((d+1)/d). Substitute 1 for d to get log(2). Since log(2) = 0.30, the probability that the number 1 is the leading digit is about 30%.

Which equation is equivalent to (1/9)^a+1 = 81^a+1 * 27^2-a ?

a. -4

If 8^y = 16^y+2, what is the value of y?

a. -8

For what value of x does 4^x = (1/8)^x+5 ?

b. -3

For what value of a does (1/7)^3a+3 = 343^a-1 ?

b. 0

For what value of x does 3^2x = 9^3x-4 ?

b. 2

If 2^2x = 2^3, what is the value of x?

b. 3/2

If 36^12-m = 6^2m, what is the value of m?

b. 6

Which expression is equivalent to log18 - log(p + 2)?

b. log 18/p+2

For what value of y does 125 = (1/25)^y-1 ?

d. -1/2

Which equation is equivalent to 2^4x = 8^x-3 ?

d. 2^4x = 2^3x-9

Which equation is equivalent to (1/3)^x = 27^x+2 ?

d. 3^-x = 3^3x+6

What is log15(2^3) rewritten using the power property?

d. 3log(15^2)

What is the solution to log2 (2x^3-8)-2log2 x=log2 x

x=2

What is the solution to log5 (10x-1)=log5 (9x+7)

x=8

How can you use transformations to graph this function? y = 3 * 7^-x + 2

*Sketch the graph of y = 7^x *Reflect the graph across the y-axis to show the function y = 7^-x *Stretch the graph vertically by a factor of 3 to show the function y = 3 * 7^-x *Shift the graph up 2 units to show the function y = 3 * 7^-x + 2

What is the approximate value of x in the equation below. log3/4^25 = 3x - 1

A -3.396

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.

A -5.95

If 8^y = 16^y+2, what is the value of y

A -8

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? L = 10log(l/l0) L = loudness, in decibels l = sound intensity, in watts/m^2 l0 = 10^-12 watts/m^2

A 0.25

Given log4^3 is approximately 0.792 and log 4^21 is approximately 2.196, what is log4^7?

A 1.404

What common base can be used to rewrite each side of the equation 2^x+3 - 3 = 5?

A 2

Which logarithmic equation is equivalent to 8^2 = 64?

A 2 = log8^64

The population of a town grew from 20,000 to 28,000. The continuous growth rate is 15%. The equation 20,000e^0.15t = 28,000 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.

A 2 years

Carlene is saving her money to buy a $500 desk. She deposits $400 into an account with an annual interest rate of 6% compounded continuously. The equation 400e^0.06t = 500 represents the situation, where t is the number of years the money needs to remain in the account. About how long must Carlene wait to have enough money to buy the desk? Use a calculator and round your answer to the nearest whole number.

A 4 years

The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as L = 10logl/l0, where l0 = 10^-12 and is the least intense sound a human ear can hear. Brandon is trying to take a nap, and he can barely hear his neighbor mowing the lawn. The sound intensity level that Brandon can hear is 10^-10. Ahmad, Brandon's neighbor that lives across the street, is mowing the lawn, and the sound intensity level of the mower is 10^-4. How does Brandon's sound intensity level compare to Ahmad's mower?

A Brandon's sound intensity is 1/4 the level of Ahmad's mower.

What are the domain and range of f(x) = logx-5

A domain: x > 0; range: all real numbers

Which function represents a vertical stretch of an exponential function?

A f(x) = 3(1/2)^x

Which expression results when the change of base formula is applied to log4(x+2)?

A log(x+2)/log4

Which of the following is equivalent to log^(1/9)/k?

A log^1/9 - logk

Which expression can be used to approximate the expression below, for all positive numbers a, b, and x, where a cannot equal 1 and b cannot equal 1? logaX

A logbX/logbA

Which statement best describes the domain and range of p(x) = 6^-x and q(x) = 6

A p(x) and q(x) have the same domain and the same range

Jillana takes a single dose of medication that remains in her body according to the equation r = 200(0.75)^d, where r represents the amount of medication remaining after d days. If Jillana had taken the medication two days earlier, the amount of medication remaining in her system relative to the amount that remains in her system after d days would be represented using the equation r2 = 200(0.75)^d + 4. Which of the following is an equivalent equation?

A r2 = 63.28(0.75)^d

Which statement is true for log3(x+1) = 2?

A x + 1 = 3^2

What is the solution to the equation e^3x = 12? Round your answer to the nearest hundredth.

A x = 0.83

What is the solution to 3 + 4e^x+1 = 11

A x = ln2 - 1

What is the value of x if e^3x+6 = 8?

A x = ln8-6/3

What is the domain of the function y = 3 ln x graphed below?

A x > 0

Which of the following is the inverse of y = 6^x

A y = log6X

Consider the equation below. log4(x+3) = log2(2+x) Which system of equations can represent the equation?

A y1 = log(x+3)/log4 , y2 = log(2+x)/log2

What is the product of (3y^-4)(2y^-4)

A 6/y^6

Which of the following describes the transformations of g(x) = -2(2)^x+4 - 2 from the parent function f(x) = 2^x

A shift 4 units left, reflect over the x-axis, shift 2 units down

Describe how (2^3)(2^-4) can be simplified

Add the exponents and keep the same base. Then find the reciprocal and change the sign of the exponent.

Tenisha solved the equation below by graphing a system of equations. log35x = log5(2x+8) Which point approximates the solution for Tenisha's system of equations?

B

If 5^3b-1 = 5^b-3, what is the value of b

B -1

For what value of x does 4^x = (1/8)^x+5

B -3

What is the value of log 43? Use a calculator. Round your answer to the nearest tenth.

B 1.6

The amount of radioactive element remaining, r, in a 100-mg sample after d days is represented using the equation r = 100(1/2)^d/5. What is the daily percent of decrease?

B 12.94%

The half-life of a radioactive element is five years. A scientist has 18 grams of the element. The equation representing the number of grams, g, after x years is g = 18(0.5)^x/5. What is the annual rate of decay?

B 13%

The amount of a sample remaining after t days is given by the equation P(t) = A(1/2)^t/h , 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?

B 2.5 mg

The graph shows the decibel measure for sounds depending on how many times as intense they are as the threshold of sound. Noise in a quiet room is 500 times as intense as the threshold of sound. What is the decibel measurement for the quiet room?

B 28 decibels

if 2^2x = 2^3, what is the value of x

B 3/2

If 36^12-m = 6^2m, what is the value of m

B 6

A business owner opens one store in town A. The equation p(x) = 10,000(1.075)^t represents the anticipated profit after t years. The business owner opens a store in town B six months later and predicts the profit from that store to increase at the same rate. Assume that the initial profit from the store in town B is the same as the initial profit from the store in town A. At any time after both stores have opened, how does the profit from the store in town B compare with the profit from the store in town A?

B 96%

What are the domain and range of f(x) = (1/5)^x

B The domain is all real numbers. The range is all real numbers greater than zero.

Which statement best describes the domain and range of f(x) = -(7)^x and g(x) = 7^x

B f(x) and g(x) have the same domain but different ranges

Tyler applied the change of base formula to a logarithmic expression. The resulting expression is shown below. (log1/4)/log12 Which expression could be Tyler's original expression?

B log12^1/4

What is 2(log3^8+log3^Z) - log3(3^4-7^2) written as a single logarithm?

B log3^2z^2

What is 2log5(5x^3) + 1/3log5(x^2+6) written as a single logarithm?

B log5(25x^6)3 squareroot of x^2 + 6

Which expression is equivalent to log8^4a(b-4/c^4)?

B log8^4 + log8^A + (log8(b-4)-4log8^C)

The estimated number of organisms in a population after t days is shown in the table below. Which equation best models the situation?

B n = 600(1.2)^t

Which of the following shows the extraneous solution to the logarithmic equation log7(3x^3+x) - log7(x) = 2?

B x = -4

What is the solution to log2(2x^3-8) - 2log2^X = log2^X?

B x = 2

What is the true solution to 3 ln 2 + ln 8 = 2 ln(4x)?

B x = 2

Which of the following shows the true solution to the logarithmic equation below? log(x) + log(x+5) = log(6x+12)

B x = 4

What is the solution to log2(9x) - log2^3 = 3?

B x = 8/3

Which equation is equivalent to logx^36 = 2

B x^2 = 36

Which function is graphed below?

B y = 3(1/3)^x

The graph of y = e^x is transformed as shown in the graph below. Which equation represents the transformed function?

B y = e^x + 3

Which of the following is the inverse of y = 3^x

B y = log3X

Which system of equations could be graphed to solve the equation below? log(2x+1) = 3x-2

B y1 = log(2x+1) , y2 = 3x-2

What are the domain and range of the function f(x) = 3^x + 5

B domain: (-infinity,infinity); range: (5,infinity)

The two expressions below have the same value when rounded to the nearest hundredth. What is the approximate value of to the nearest hundredth?

B. 1.23

Nolan began a savings account three years ago. He invested $100 at a 2% interest rate according to the equation Vn = 100(1.02)x, where Vn is the value of his account after x years. Anias started an account today. She invested $100 at a 2% interest rate according to the equation Va = 100(1.02)x-3, where Va is the value of her account. Let's say Anias started saving at the same time Nolan did, three years ago. Approximately how much money would she have had to invest to have the same amount of money she has now?

C $94.23

What is the value of log 13? Use a calculator. Round your answer to the nearest tenth

C 1.1

Kim solved the equation below by graphing a system of equations. log2(3x-1) = log4(x+8) What is the approximate solution to the equation?

C 1.4

Given log3^2 is approximately 0.631 and log 3^7 is approximately 1.771, what is log3^14?

C 2.402

What is the value of log27^9

C 2/3

Which equation is equivalent to log3(x+5) = 2

C 3^2 = x + 5

If 3^2x+1 = 3^x+5, what is the value of x

C 4

What is the value of log3^81

C 4

On a piano, the formula to determine the frequency of any pitch relative to the A above middle C (A440) is given by the expression f(x) = 440(2)^x/12 , where x represents the the number of half-steps above or below A440. Which of the following is equivalent to f(x)?

C 440 * 12 squareroot of 2^x

The amount of a sample remaining after t days is given by the equation P(t) = A(1/2)^t/h , 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?

C 74 days

What is the value of e^ln7x?

C 7x

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 2 x 10^-9?

C 8.7

Which properties are present in a table that represents a logarithmic function in the form y = logbX when b > 1 I. The y-values are always increasing or always decreasing. II. The point (0, 1) exists in the table. III. The y-values will decrease rapidly as the x-values approach zero. IV. There will only be one x-value in the table with a y-value of zero.

C I, III, and IV

Anja simplified the expression 10x^-5/-5x10 to 15/x^15. What mistake did Anja make

C She subtracted the coefficients instead of dividing them

The equation for the pH of a substance is pH = -log[H+], where H+ is the concentration of hydrogen ions. Which equation models the concentration of hydrogen ions (H+) of a solution whose pH is 7.2?

C [H+] = 10^-7.2

The function f(h) = m(1/2)^h gives the mass, m, of a radioactive substance remaining after h half-lives. Cobalt-60 has a half-life of about 5.3 years. Which equation gives the mass of a 50 mg Cobalt-60 sample remaining after 10 years, and approximately how many milligrams remain?

C f(x) = 50(0.877)^10 ; 13.5 mg

Which logarithmic equation has the same solution as x-4 = 2^3?

C log2(x-4) = 3

Which expression is equivalent to log3(x+4)?

C log3 + log(x+4)

Which expression is equivalent to log3^c/9

C log3c - log3(9)

Which of the following shows the equation log4(x+6) = 2 rewritten using logarithms?

C log4(x+6) = log4^16

Sam is proving the product property of logarithms. Which expression and justification completes the third step of her proof?

C logb(b^x+y); power rule of exponents

The proof for the power property of logarithms appears in the table with an expression missing. (step 3/6) Which expression is missing from the proof?

C logb(b^xy)

Jenny invests $2,000 at an interest rate of 5%. The amount of money, Ma, in Jenny's account after t years can be represented using the equation Ma = 2000(1.05)^t . If Jenny would have invested the same amount of money at the same interest rate four years ago, the equation representing the amount of money, Mb, in her account would be represented using the equation Mb = 2000(1.05)^t+4. Which of the following is equivalent to ?

C mb = 2000(1.05)^t(1.05)^4

What is the domain of the function y = ln(-x+3/2)?

C x < 3

What is the true solution to 2 ln 4x = 2 ln 8?

C x = 2

What is the solution to log3(x+12) = log3(5x)?

C x = 3

Which of the following shows the extraneous solution to the logarithmic equation? log4(x) + log4(x-3) = log4(-7x+21)

C x = 3 and x = -7

Maria wrote the equation log(x/2) + log(20/x^2) = log8. What is the solution to Maria's equation?

C x = 5/4

Which expression is equivalent to (3^2)^-2

C 1/81

Which expression is equivalent to 9^-2

C 1/81

What is the quotient of 7^-1/7^-2

C 7

Leela invests $500 at 4.5% interest according to the equation Vl = 500(1.045)^t , where Vl is the value of the account after t years. Adele invests the same amount of money at the same interest rate, but begins investing two years earlier according to the equation Va = 500(1.045)^t+2. The total value of Adele's account is approximately what percent of the total value of Leela's account at any time, t?

D 109.2%

What is the value of log7^343

D 3

What is log15^2^3 rewritten using the power property?

D 3log15^2

A scientist has 50 grams of a radioactive element. The amount of radioactive element remaining after t days can be determined using the equation f(t) = 50(1/2)^t/5 . After two days the scientist receives a second shipment of 50 grams of the same element. The equation used to represent the amount of shipment 2 remaining after t days is f(t) = 50(1/2)^t-2/5 . Which of the following is an equivalent form of the expression for the amount remaining in shipment 2?

D 50 * 5 squareroot of (1/2)^t , divided by (1/2)^2/5

The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as L = 10logl/l0, where l0 = 10^-12 and is the least intense sound a human ear can hear. What is the approximate loudness of a dinner conversation with a sound intensity of 10^-7?

D 50 Db

For what value of b does (1/12)^-2b * 12^-2b+2 = 12

D No solution

Sebastian used the table and correctly identified that the data does not represent a logarithmic function. What information did Sebastian use in his deduction?

D The table shows two x-intercepts and it changes from increasing to decreasing

Which of the following illustrates the product rule for logarithmic equations?

D log2(4x) = log2^4 + log2^X

Devonte used the change of base formula to approximate log8^25. Which expression did Devonte use?

D log25/log8

Which equation has x = -6 as the solution?

D log3(-2x-3) = 2

What is log5(4*7) + log5^2 written as a single log?

D log5^56

When proving the product, quotient, or power rule of logarithms, various properties of logarithms and exponents must be used. Which property listed below is used in all of these proofs?

D logb(b^y) = y

Which is equivalent to log2^17 = 4?

D logn = 4log2

An antibiotic kills 60% of bacteria in a sample of 100,000 each day. The equation p1 = 1000,000(0.4)^d represents the population, p1, after d days. Four days after introducing the antibiotic to the first sample, a scientist introduces the same antibiotic to a second population, p2. The number of bacteria after d days in the second population is represented by the equation p2 = 100,000(0.4)^d-4. Which equation is equivalent to p2?

D p2 = 3,906.250(0.4)^d

Which of the following describes the transformation of g(x) = 3(2)^-x + 2 from the parent function f(x) = 2^x

D reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up

What is the true solution to the logarithmic equation below? log4[log4(2x)] = 1

D x = 128

What is the solution to the equation below? log20x^3 - 2logx = 4

D x = 500

What is the solution to 4^log4(x+8) = 4^2

D x = 8

What is the solution to log5(10x-1) = log5(9x+7)?

D x = 8

Identify the equation that translates y = ln(x) five units down.

D y = ln(x) - 5

Which function is shown in the graph below

D y = log6X

Which system of equations could be graphed to solve the equation below? log0.5X = log3^2 + x

D y1 = logx/log0.5 , y2 = log2/log3 + x

Omar wants to use a graph to solve the equation below. log6X = log2(x+4) Which system of equations should Omar use?

D y1 = logx/log6 , y2 = log(x+4)/log2

What is the quotient of -8x^6/4x^-3

D -2x^9

Which expression is equivalent to 5y^3/(5y)^-2

D 125y^5

Which of the following is equivalent to log (1/9)/k?

a. log1/9 -logk

Graph a system of equations to approximate the value of x, the rate of depreciation. Give your answer as a percent.

( B ) about 13%

Which of the following describes the transformation of mc021-1.jpg from the parent function mc021-2.jpg?

(D) reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up

Graph a system of equations to solve log (−5.6x + 1.3) = −1 − x. Round to the nearest tenth. From the least to the greatest, the solutions are:

-2.1 0.2

Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10%. The second car depreciates at an annual rate of 15%. What is the approximate difference in the ages of the two cars?

1.7 years

Consider the equation log5(x + 5) = x2. What are the approximate solutions of the equation? Check all that apply.

A D

One brand of vinegar has a pH of 4.5. Another brand has a pH of 5.0. The equation for the pH of a substance is pH = -log[H+], where H+ is the concentration of hydrogen ions. What is the approximate difference in the concentration of hydrogen ions between the two brands of vinegar?

A. 2.2*10^-5

Which of the following shows the extraneous solution to the logarithmic equation below?

A. x=-6

What is the range of the function f(x) = -2(6x) + 3?

B. - infinity, 3

If , what is the value of x?

B. 8/5

What is the solution of logx729=3

B. 9

What are the domain and range of mc017-1

B. domain: x > 1; range: all real numbers

What is rewritten using the power property?

B. floge

What is written as a single logarithm?

B. log base 1/2 w^4 (u^2/v^3)

Which expression is equivalent to 5y^-3

C 5/y^3

Choose the letter of the expression listed on the right that completes each step to show how to use the power and product properties of logarithms to prove that the quotient property is true for logbxy. logb xy

CADB

Devonte used the change of base formula to approximate log825. Which expression did Devonte use?

D

Omar wants to graph the system of equations below. log6x = log2(x+4) Which system of equations should Omar use?

D

Which is equivalent to log2n = 4?

D

Which is the graph of y=-log(x-2)+3

D

What is the quotient of 2^4/2^-4

D 256

Elsa tries to solve the following equation, and determines there is no solution. Is she correct? Explain. log2x = log2(3x + 5) + 4

Elsa tries to solve the following equation, and determines there is no solution. Is she correct? Explain. log2x log2(3x 5) 4

Which logarithmic equation has the same solution as x-4=2^3

Log2 (x-4)=3

Consider the equation below. log4(x=3)=log2(2+x) Which system of equations can represent the equation?

NOT B

Kim solved the equation below by graphing a system of equations. log2(3x-1) = log4(x+8) What is the approximate solution to the equation?

NOT BD

Which statement best describes the domain and range of f(x) = -(7)x and g(x) = 7x?

NOT C

Given log4(3) = 0.792 and log4(21) = 2.196 what is log4(7)?

a. 1.404

Which expression is equivalent to log12 (1/2 / 8w)?

b. log(12^1/2) - (log12^8 + 12w)

Which expression is equivalent to log(8^4a) (b-4)/c^4)?

b. log(8^4) + log(8^4) + log(8(b-4)-4log(8^c)

What is 2(log(3^8)+ log3(3^4 - 7^2)) written as a single logarithm?

b. log3(2z^2)

What is 2log5(5x^3) + 1/3 log5 (x^2 + 6) written as a single logarithm?

b. log5(25x^6)3√x^2 + 6

Which expression is equivalent to log6(4a) (b-4/c^4)?

b. log8(4) + log8(a) +(log8(b-4)-4log8c)

Given log(3^2)= 0.631 and log(3^7)= 1.771, what is log(3^14)?

c. 2.402

Which equation is equivalent to 16^2p = 32^p+3 ?

c. 2^8p = 32^p+3 ?

If 3^2x+1 = 3^x+5, what is the value of x?

c. 4

Which expression is equivalent to logw (x^2 -6)^4 / 3√x^2 + 8) ?

c. 4logw(x^2 -6) - 1/3 logw(x^2 + 8)

Which expression is equivalent to log3(x + 4)?

c. log3 + log(x + 4)

Which expression is equivalent to log3 (c/9)?

c. log3 c - log3(9)

Which expression is equivalent to logc (x^2 - 1)/5x ?

c. logc (x^2 - 1)-(logc5 + logcx)

If 12^x^2+5x+4 = 12^2x+6, what could be the value of x?

c. x = 2, x = -5

The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as L= 10log I/I(0), where I(0) = 10^-12 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?

d. 50 Db

What is log5(4 * 7) + log(5^2) written as a single log?

d. log(5^56)

For what value of b does (1/12)^-2b * 12^-b+2 = 12 ?

d. no solution

log6 216=3 or 6^3=216,,loga x=logbx/logba

domain expo real numbers,range expo +real numbers,exp y only,increasing domain,asymptote x axis

Write the following expression as a single logarithm with coefficient 1. log910 − log9 12 − log94

log 9(5)

Expand: log20 mn5p

log20m-5log20n-log20p

Complete the steps to evaluate the following expression, given log3a = −0.631. log3 a3

log3(3)= log3(a/3)=-1.631

Write the following expression as a single logarithm with coefficient 1. log3(6c) + log3112

log3(c/2)

Rewrite the following expression as a single logarithm with coefficient 1. 3log5 uv2w3

log5(u^3v^6/w^9)

Complete the steps to evaluate log798, given log72 ≈ 0.356. How can you rewrite log798 using the product property?

log7(2)+log7(49) log7(49)=2 log7(98)=2.356

The proof for the product property of logarithms requires simplifying the expression logb(bx+y) to x + y. Which property is used to justify this step?

logb(b^c)=c

Use the properties of logarithms to write the following expression as one logarithm. logslogr + 8logr s − 3logr t

logr(s9/t3)

A student showed the steps below while solving the equation by graphing. Step 1:Write a system of equations: Step 2: use the change of base formula to rewrite the equations:

step 2

bob

the

Which statement is true for log3 (x+1)=2

x+1=3^2

Use the change of base formula to approximate the solution to log0.515 = 1 - 2x. Round to the nearest hundredth.

x= 2.45

Which of the following shows the extraneous solution to the logarithmic equation? log4 (x)+log4 (x-3)=log4 (-7x+21)

x=3 and x=-7

Which of the following shows the true solution to the logarithmic equation below? log(x)+log(x+5)=log(6x+12)

x=4

Maria wrote the equation log(x/2)+log(20/x^2)=log8 What is the solution to Maria's equation?

x=5/4

Which of the following is true regarding the solutions to the logarithmic equation below?

x=6 is a true solution and x=-6 is an extraneous solution

What is the solution to log2 (9x)-log2 3=3

x=8/3