Basic Math question and answers for September 25, 2024
- Q Solve the following logarithmic equation.log (4x+6)= 1+ log (x - 5)Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A. The solution set...
- Q Use the properties of logarithms to write the expression as a single logarithm. Assume that all variables are defined in such a way that the variable expressions are positive.log9(x+5)+ log9(x+3)log9(x...
- Q Solve for x:log6 (3x + 10) = 2Write log6 (3x + 10) = 2 in exponential form._________________Find the value of x.x= ___________
- Q e^(2x+1)=48Write the equation as an equation involving logarithms._______________Find the solution of the equation in terms of logarithms, or correct to four decimal places.x=______________
- Q Which is the logarithmic form of the given equation?10? = 1000? log 10 = x? log x = 10? log 1000 = x? log x = 1000
- Q Graph f(x)=-2 log3 (x) + 5 using transformations by first graphing the basiclogarithmic function (parent function), then the progression of transformations (in thecorrect order). State the domain, range, and vertical...
- Q Use the Change of Base Formula to evaluate log3 48. Then convert log3 48 to a logarithm in base 5. Round to the nearest thousandth.3.524; logs 290.3853.524; logs 803.871; logs...
- Q What is the domain and range of this function?f(x) = logg(x-2) + 1A domain: x > -2; range: all positive real numbersB domain: x> 2; range: all positive real numbersC...
- Q Expand the following expression: ln r/xy?a. 3 In (r) + 2 In (x) -5 In (y)b. 3 In (r) - 2 In (x) - 5 In (y)c. 3 In (r)...
- Q The profits for a company can be modeled by the logarithmic functionP(t) = (3/2)log(2t + 1) With P in thousands of dollars and tin years. What is the average increase...
- Q How much more intense is an earthquake of magnitude 3.6 than an earthquake of magnitude 1.8?a) 63 times more intenseb) twice as intensec) 100 times more intensed) 1.8 times more...
- Q Which statement is TRUE for the graph of the logarithmic function f(x) = log?x:a) There is a horizontal asymptoteb) The graph only exists above the x-axisc) The graph only exists...
- Q Express as a single logarithm and simplify;log?6+log?1.5a) 0b) 1c) 2d) log?7.5
- Q Expand the logarithmic expression.log? x?/5y6log?x - log?5 + log?y6log?x - log?5-log? y6log? x + log? 5 + log?y 6log?x - 5log?y
- Q Condense the logarithmic expression.log?6+3log?3-log?9a log?153b log?24c log?6d log?18
- Q The magnitude of an earthquake is measured on the Richter scale as a logarithm of the intensity of the shock wave. For magnitude R and intensity I, the formula is...
- Q What is the solution to this equation?log(2x 100) = 3A. x= 100B. x= 550C. x= 1,000D. x= 450
- Q Let a = log2 3, b= log2 5 and c=log? 7,A. Write the following in terms of a, b and ci. (K:2) log? (45): 2a+b-cii. (K:2) log? (52.5): a+b+c-1B. (1:2)...
- Q Use a calculator to find the following natural logarithm.In 67In 67=(Round to four decimal places as needed.)
- Q Solve the equation for x.log8(x+3)-log8(x)=log8(25)x=__
- Q Use the Quotient Rule of Logarithms to write an expanded expression equivalent to log2(4x+1/x). Make sure to use parenthesis around your logarithm functions log(x + y).Note: If you are using...
- Q There was a sample of 700 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 3.1% each year. Let t be the number...
- Q Use the Product Rule of Logarithms to write the completely expanded expression equivalent to log(8(1 + 3x)). Make sure to use parenthesis around your logarithm functions log(x + y).
- Q Write the following as the sum and/or difference of logarithms. Assume all variables are positive.log (10z/4)= __The answer format in lowercase characters is: log(number)Spaces in the answer are optional.
- Q The pH scale was designed to make it convenient to express hydrogen ion concentrations that are small in aqueous solutions. The definiton of pH is in terms of base 10...
- Q Use the power property to rewrite each expression. Assume all variables are positive.log, (a-4)=The answer format in lowercase characters is: log_base (number)Spaces in the answer are optional.
- Q Find the solution of the exponential equationex+1= 32in terms of logarithms, or correct to four decimal places.x=
- Q Which expression and justification completes the third step of her proof?(A) log, (b^(xy)); power rule of exponents(B) log,(b^(x-y)); subtraction property of exponents(C) log(b^(x+y)); power rule of exponents(D) log, (b^(x/y)), division...
- Q A student solved the equation below by graphing.log6(x-1)= log?(2x+2)Which statement about the graph is true?The curves do not intersect.The curves intersect at one point.The curves intersect at two points.The curves...
- Q Find the equation of the function that is finally graphed after the following transformations are applied to the graph of y = 3? (write your resulting transformation in every step...
- Q Simplify the expression without using a calculator.log? 4.
- Q Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. Assume that the variables represent positive real numbers.log? (x/yz).
- Q Write the expression as a sum and/or a difference of logarithms with all variables to the first degree. log [9w(v + 4)](A) log 9+ log w+ log v + log...
- Q Find fx and fy for f(x,y) = y In (3x+8y).
- Q The relationship between water content (w%) and number of blows (N) in soils, as obtained from Casagrande's liquid limit device, is given byw = 20-log10 NThe liquid limit of soil...
- Q Using y(t) = 110ekt, and the fact that y(30)= 75, we can solve for k.y(t) = 110ekty(30) =110ek.=110ekThus, we have the following equation.k =
- Q Rewrite the expression as an equivalent ratio of logs using the indicated base.log13 (57.25) to base 10
- Q Expand the logarithm as much as possible by rewriting it as a sum, difference, or product of logarithms.log4(x/z / w)
- Q The half-life of a certain tranquilizer in the bloodstream is 34 hours. How long will it take for the drug to decay to 87% of the original dosage? Use the...
- Q Solve the logarithmic equation. Be sure to reject as a solution any value that is not in the domain of the original logarithmic expressions.2 log x = log 25Solve the...
- Q Solve the following system.logy x=4logy (16x) = 6Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A The solution set is(Type an ordered...
- Q Write the equation in its equivalent exponential form. Then solve for x.log 4(x-4) = 2log 4(x-4) = 2 in its equivalent exponential form is. (Do not simplify.)x=
- Q Which of the following is the inverse of y=12x?y = log1/12 xy = log12 1/xy=logx12y = log12X
- Q Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 1400 bacteria selected from this population reached the size...
- Q Use the Change of Base Formula to evaluate log4 27. Then convert log4 27 to a logarithm in base 2. Round to the nearest thousandth.3.296; log? 5.1962.377; log? 13.52.377; log?...
- Q Suppose a house that costs $270,000 appreciates by 5% each year. In about how many years will the house be worth $350,000? Use the equation 350 = (270)(1.05)* and round...
- Q Suppose a new car that costs $25,000 depreciates by 12% each year. In about how many years will the car be worth $15,000? Use the equation 15,000 = (25,000)(0.88)^x and...
- Q The population of a certain city was 3,674 in 1995. It is expected to decrease by about 0.31% per year. Write an exponential decay function, and use it to approximate...
- Q Identify the error in the student solution shown below. Find the correct answer.2ln(x) = In(3x) - [In(9) - 2ln(3)]In(x)= In(3x) - [In(9) - In(9)]In(x)= In(3x)-0In(x)= In(3x/0); division by 0, undefined.
- Q The rabbit population of Springfield, Ohio was 144,000 in 2016. It is expected to decrease by 7.2% per year.Write an exponential function and use it to predict the rabbit population...
- Q Rewrite In 5 + ln 7 as a In single logarithm.
- Q Find the exact value of the logarithm without using a calculator.log 5 125
- Q A wooden artifact from an ancient tomb contains 55 percent of the carbon-14 that is present in living trees. How long ago, to the nearest year, was the artifact made?...
- Q A wooden artifact from an ancient tomb contains 35 percent of the carbon-14 that is present in living trees. How long ago, to the nearest year, was the artifact made?...
- Q Let P(t) = 30000 (1.03)t be the population of a town t years after the year 2000.Estimate in which year the population will reach 32782.Year =
- Q In 2009, an earthquake hit Costa Rica, registering a 6.1 on the Richter scale. What was the intensity of this earthquake, assuming the reference value was 1?(R =log(I/I?))A. 5.1B. 4.46...
- Q In a learning theory project, psychologists discovered thatf(t) = 0.8 / (1+e^-0.2t)is a model for describing the proportion of correct responses, f(t), after t learning trials.a. Find the proportion of...
- Q 1. The logistic growth function f(t) = 100,00 / (1 + 5000e-t) describes the number of people, f(t), who have become ill with influenza t weeks after its initial outbreak...
- Q Where is the function defined by f(x)= In (x) increasing? Where is f(x) decreasing? Where is the tangent line horizontal?Where is f(x) increasing? Select the correct choice below and, if...
- Q Use properties of logarithms to rewrite the given expression as the logarithm of a single quantity, then enter that single quantity in the answer box to complete the expression.2 logb...
- Q Solve the following logarithmic equation. Use a calculator if appropriate.log (4x+3)+ log 2 = log (7x+8)Select the correct choice below and, if necessary, fill in the answer box to complete...
- Q In July 2005, the internet was linked by a global network of about 352.8 million host computers. The number of host computers has been growing approximatelyexponentially and was about 36.9...
- Q Condense the following expressions into a single logarithm by applying the properties of logarithms.Make sure your final answer is written as a single logarithm.a. 2 log(x) - 5 log(y) +...
- Q Expand and simplify the following expression.log? (4x3/y2z4)2+3 log? (x)-2 log2(y)-4 log2(z) 2+log3(x)-log2(v)-log4(z) 2+3 log3(x)-2 log(y) - 4 log(z)2+3 log2(x)-2 log2(v) +4 log2(z)
- Q Obtain an approximate value for the logarithm using natural logarithms.log 5313log 5313(Round to three decimal places as needed.)
- Q (a) Solve the equation 1500(0.733)t = 300 using the In function.Round your answer to three decimal places.(b) Solve the equation 1500 (0.733)t = 300 using the log function.Round your answer...
- Q A certain culture of bacteria initially has 10 bacteriaand is observed to double every 1.5 hours.a. Find an exponential model n(t) =n0*2/a for thenumber of bacteria in the culture after...
- Q Solve the exponential equation. Express irrational solutions as decimals correct to the nearest thousandth.(1/2)x = 13Select the correct choice below and, if necessary, fill in the answer box to complete...
- Q Solve the equation. Write the answer in terms of the natural logarithm.e9x + 4 = 6The solution set is.(Type an exact answer in simplified form. Use integers or fractions for...
- Q Express the following equations in logarithmic form:(a) 5^4 = 625 is equivalent to the logarithmic equation:(b) 10^ 3 =0.001 is equivalent to the logarithmic equation:
- Q Rewrite the expression e^5 ln(x) so that no exponential or logarithmic functions are involved. The formula b^ln t = r and the basic rules of exponents will be helpful. Assume...
- Q Choose a number between 0 and 100 for k. Enter your number in the blank so I know what to use for grading. k=__. Rewrite each exponential equation in logarithmic...
- Q Use logarithms to solve the given equation. (Round the answer to four decimal places.)3^-2x = 43X=
- Q Find the associated exponential decay or growth model. (Round all coefficients to three significant digits.)Q = 1,600 when t = 0; half-life = 1Q =
- Q The yield V (in millions of cubic feet per acre) for a stand of timber at age t isV = 6.8e^(-4.85)/twhere t is measured in years.(a) Find the limiting volume...
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