Basic Math question and answers for September 24, 2024
- Q Use the properties of logarithms to completely expand log 3 11y7/pDo not include any parentheses in your answer.Note: If you are using log you need to type it in and...
- Q Write the following as a single logarithm.log3 (4xy) + log3 (5xy)
- Q Using the definition of the logarithm, what expression should go in the blank below?54 = 6254 =Provide your answer below:
- Q Evaluate log5 1/25 Write your answer in simplest form.Provide your answer below:
- Q Use the change of base formula to express log6 8 using log, the common logarithm. Note: If you are using log you need to type it in and use the...
- Q QuestionWhich of the following equations uses the inverse property of logarithms correctly?Select all correct answers.Select all that apply:? 50g, (9)? 5log5 (9) 9glog5 (5) = 55log, (5) 9log5 (95) =...
- Q Solve 9e7x = 17.Round your answer to the nearest tenth. Do not include "=" in your answer. If necessary, include a leading 0 with any decimals less than 1. For...
- Q Enter the single simplified logarithm expression which is equivalent to 3 In 10-4 In 2 - In 5.Note: When entering natural log in your answer, enter lowercase LN as "In"....
- Q Write log, A as a natural logarithm.Note: When entering natural log in your answer, enter lowercase LN as "in". There is no "natural log" button on the Alta keyboard.
- Q Rewrite e^x = 20using natural logs
- Q Solve the equation. Write the solution set with the exact values given in terms of common or natural logarithms. Also give approximate solutions to at least 4 decimal places.6e^3n-2+3=15
- Q Graph f(x) = log5 (x) + 4 using transformations by first graphing the basic logarithmicfunction (parent function), then the progression of transformations (in the correct order).State the domain, range, and...
- Q Express the following equations in logarithmic form:(a) 4 = 256 is equivalent to the logarithmic equation:(b) 10-2 = 0.01 is equivalent to the logarithmic equation:
- Q Rewrite each of the following equations: (Make sure to preview each answer)(a) Rewrite 4 = 64 as a logarithmic equation:(b) Rewrite log 0.0001 = - 4 as an exponential equation:
- Q The wind speed near the center of a tornado is represented by the equation S = 93 log d +65, where d is the distance, inmiles, that the tornado travels...
- Q Simplify. Enter the result as a single logarithm with a coefficient of 1.To enter the log, click in the answer cell, then click on the small yellow arrow on the...
- Q Evaluate the expression without using a calculator.log 31log 31 =(Type an integer or a simplified fraction.)
- Q Is x = 0 a valid potential solution to the equation log(x + 2) + log(x + 5) = 1? (Youdon't need to solve this equation, just determine if x...
- Q Write the equation in logarithmic form.r=sThe equation in logarithmic form is
- Q Does the function f(x) = (0.68)* represent exponential growth, decay, or neither?Impossible to determine with the information givenExponential growthNeitherExponential decay
- Q Students in a fifth-grade class were given an exam. During the next 2 years, the same students were retested several times. The average score was given by the model ...
- Q Use the Product Rule of Logarithms to write the completely expanded expression equivalent to log5 (3x + 6y). Make sure to use parenthesis around your logarithm functions log(x + y).Note:...
- Q Write the expression as a single logarithm.log4(x-4) - 6 log 4(x+2)
- Q Rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm, and then round to three decimal places.y = 1.5(1.8)^xy = (In 1.5)e^x In...
- Q An exponential decay function can be used to model the number of grams of aradioactive material that remain after a period of time. A radioactive isotope decaysover time, with the...
- Q Solve for :log(x) + log(x + 5) = 3You may enter the exact value or round to 4 decimal places.
- Q Write the following sum as a single logarithm. Assume all variables are positive.log3(c) + log3(c + 7) =The answer format in lowercase characters is: log_base (number)Spaces in the answer are...
- Q Evaluate using your calculator and round to 4 decimal places.log14(41)=
- Q Bacteria are growing exponentially in an environment of unlimited space and food. Thedoubling time is 1 hour.a. If there are initially a milligrams of bacteria, express the mass of the...
- Q (a) Let B=5750(1.045) give the balance of a bank account after t years. If the formula for B is written B=5750e, estimate the value of k correct to four decimal...
- Q Solve the exponential equation. Leave your answer in exact form.7* = 53The exact solution is x = 0.(Type an exact answer in simplified form.)
- Q Use the laws of logarithms to find the exact value of the expression 2 In (8e) - In (64) without using a calculator.(Give an exact answer. Use symbolic notation and...
- Q Write in exponential form.-3= log 9 (1/729)The logarithmic equation - 3= log g1729is the same as the exponential equation
- Q Give the starting value a, the growth/decay rater, and the continuous growth/decayrate k. If there is exponential is decay your growth rates should be negative. For helpentering logarithms, see help...
- Q Solve the logarithmic equation.1132log b3 =b= (Type an integer or a simplified fraction.)
- Q Give the growth factor b, the starting value a, the growth rate r, and the value of kwhenQ is written in the form Q = a ekt. If there is...
- Q Rewrite the following statement using a natural logarithm. Fillin each blank with the appropriate letter or number.? 0.0183 is equivalent to In (
- Q The sales of lawn mowers t years after a particular model is introduced is given by the function y = 5500 In (9t + 4), where y is the number...
- Q 8.5^-t/9= 346Which of the following is the solution of the equation?Choose 1 answer:At = 9 log346 (40)t= -9 log5 (43.25)t = 9 log5 (43.25)t = -9 log40 (346)
- Q A 33 gram sample of a substance that's used to detect explosives has a k-value of 0.1473.N= Noe^-ktN0= initial mass (at time t = 0)N= mass at time tk=a positive...
- Q A country's population in 1994 was 76 million. In 1998 it was 81 million. Estimate the population in 2016 using the exponential growth formula. Round your answer to the nearest...
- Q The decibel rating D is related to the sound intensity I by the formula D = 10 log10(I/10^-16)for the noise level in decibels.(a) Let D and d represent the decibel...
- Q A country's population in 1995 was 32 million. In 1997 it was 34 million, Estimate the population in 2003 using the exponential growth formula. Round your answer to the nearest...
- Q Find an approximate irrational solution to 3* = 7....Select the correct choice below and, if necessary, fill in the answer box to complete your choice.OA. The solution set is }....
- Q ARewrite the logarithmic equation log(+2) = 2 in equivalent exponential form. There may be more than one correct answerAz+2=e2B.z+2=100DC. e+2=D.z+2=10DE 2+2 = log(2)F. None of the above
- Q Expand the logarithm fully using the properties of logs. Express the final answer in terms of log x, log y, and log z.logx^5/?zy
- Q Write the log equation as an exponential equation. You do not need to solve for x.log(x-3) (x)=9/5
- Q Suppose the supply of x units of a certain product at price p dollars per unit is given byp = 12 + 6 In(4x + 1).How many units of this...
- Q Describe the largest set S on which it is correct to say that F is continuous.F(x,y)= In (x + y-36)Choose the correct answer for points where the function In (x...
- Q What is the meaning of the base of the functiony = log3(x)?As y increases by 1, x increases by a factor of 3.As y decreases by 1, x increases by...
- Q A culture of 100 bacteria is started, and the number of bacteria will double every hour. In about how many hours will there be over 4,000,000 bacteria? Hint: use a...
- Q Your bank account is sitting on $14,000. Youstarted with a principal balance of $12,500. If theinterest rate was 4.5% compounded continuously,how long was your money in the bank?1.12 yearsLess than...
- Q Determine f^-1(x) of f (x) = 5^(x+3) - 2.f^-1(x)= log3 (x + 2) + 5f^-1(x)= log? (x-3)f^-1(x)= log5 (x+2) - 3f^-1(x)= log5 (x - 2)
- Q Solve the following logarithmic equation.11+ log (10x+21) = 10Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A. The solution set is(Use a...
- Q The volume of a swimming pool being filled with water, in gallons, after t hours is modeled by the following function:V(t) = 22,500 - 10,000e^(-0.2t)Find the rate at which the...
- Q Use the properties of logarithms to completely expand ln 11y?/xDo not include any parentheses in your answer.
- Q In the beginning, the population of Antarctic Aardvarks was 8 million. Ever since, it has been decreasing by 8.5% every three thousand years. Write an exponential model P(t) for the...
- Q The Parker family bought a house for $140,000. The value of the real estate in that town will increase by 3.1% each year.If values continue at that rate, calculate how...
- Q The mass if Missy's megafis increases according to the exponential model:M(t) = 12(1.24)^t/7+3Where t is the number of days elapsed. By what percent does the mass of Missy's megafish increase...
- Q Suppose that $2060 is deposited into an account where the interest is compounded annually.This situation can be modeled by the functionP (t) = 2060(1.018)^t where P(t) represent the value (in...
- Q Suppose that a new employee starts working at $7.52 per hour, and receives a 4% raise each year. After time t, in years, his hourly wage is given by the...
- Q Express in terms of logarithms without exponents.log c (xy5z-9)What is the equivalent expression?
- Q Convert to a logarithmic equation.10^5 = 100,000The equation is
- Q A student was asked to determine the y-intercept for the logarithmic function f(x) = log3(x +2) + 1. Which of the following expressions would result in the correct y-intercept?log2/log3+1log3/log2+1(3)-1-2(-1)3-2
- Q Painful bone metastases are common in advanced prostate cancer. Physicians often order treatment with strontium-89 (89 Sr), a radionuclide with a strong affinity for bone tissue. A patient is given...
- Q Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible.log7(4116 )-log7(2) - log,7(42) =
- Q A can of soda is placed inside a cooler. As the soda cools, its temperature 7(x) in degrees Celsius is given by the following function, where x is the number...
- Q Using the formula R = log ( x/0.001), where x is the seismographic reading in millimeters, and R is the magnitude of the earthquake on the Richter scale, determine the...
- Q The count in a bacteria culture was 100 after 20 minutesand 1800 after 40 minutes. Assuming the count growsexponentially,What was the initial size of the culture?Find the doubling period.Find the...
- Q You go to the doctor and he gives you 10 milligrams of radioactive dye. After 24 minutes, 6.5 milligrams of dye remain in your system. To leave the doctor's office,...
- Q The half-life of Radium-226 is 1590 years. If a samplecontains 100 mg, how many mg will remain after 2000 years? ...
- Q Solve for x:4 + 5log3(x + 6) = 8Round your answer to 3 decimal places.x = -3.345No solutionx= -3.592x = 8.408
- Q Solve the following exponential equation. Express your answer as both an exact expression and a decimal approximation rounded to two decimal places. Use e = 2.71828182845905.e 3x-7 = 9 x/7
- Q Find the domain of the logarithmic function y = log (4x + 5) analytically. You may wish to check your answer graphically.The domain is ( , ?).(Simplify your answer. Type...
- Q Solve for x.log x-log(x+2) = -1Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A. The solution (s) is/are x =(Type an integer...
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