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Mathematics: Solve And Win by freemandgenius(m): 10:33pm On Dec 14, 2017 |
Hey, where are the mathematicians here. Solve this with proves- 2^x=4x. Find x . Show full workings and earn a Christmas gift from me. The first to get it with proves. |
Re: Mathematics: Solve And Win by Nobody: 11:06pm On Dec 14, 2017 |
freemandgenius: 2^x=4x, (apply log to base 10 to both side) log2^x=log(4x), xlog2=log4+logx, xlog2=log2^2+logx, xlog2=2log2+logx, (collect like terms), xlog2-2log2=logx, log2(x-2)=logx, (removin log to base from both sides ) 2(x-2)=x, 2x-4=x, 2x-x=4, x=4 x=4 4 Likes |
Re: Mathematics: Solve And Win by dejt4u(m): 11:09pm On Dec 14, 2017 |
freemandgenius:2x=4x taking log 10 of both sides; log 2x = log 4x, xlog2 = log 4 + log x, xlog2 = log 22 + log x, xlog2 = 2log2 + log x xlog2 - 2log2 = log x log2 (x - 2) = log x log will cancel each other; 2(x-2) = x 2x - 4 = x 2x - x = 4 x = 4 |
Re: Mathematics: Solve And Win by Brunicekid(m): 11:23pm On Dec 14, 2017 |
To solve 2^x=4x then Log both sides, Log 2^x=Log 4x Applying fully the Law of Logarithms for two terms in multiplication in Logs turning to addition on R. H. S. and Logarithm law on terms with power on L. H. S. then, x Log 2=Log 4+Log x x Log 2=Log 2^2 +Log x x Log 2=2 Log 2 + Log x By selecting like terms, then bring terms with Log 2 to one side and other terms to other side, x Log 2- 2 Log 2=Log x By factorising the terms on the L. H. S, (x-2) Log 2= Log x Cancelling out Log on both sides, then: (x-2)2 =x 2x-4 =x 2x-x=4 Therefore, x=4. |
Re: Mathematics: Solve And Win by thankyouJesus(m): 10:01am On Dec 15, 2017 |
Very funny The use of logarithm law is not feasible here (x-2)log2 = logx (x-2)2 = x Smiles |
Re: Mathematics: Solve And Win by thankyouJesus(m): 10:08am On Dec 15, 2017 |
Smiles 1 Like
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Re: Mathematics: Solve And Win by Nobody: 4:48pm On Dec 15, 2017 |
freemandgenius:guy, what about the Christmas Gift? |
Re: Mathematics: Solve And Win by freemandgenius(m): 6:59pm On Dec 15, 2017 |
kelvinreality:love that. You are 100% confident . Nice one. Will mail you soon for a token recharge. Drop your digits |
Re: Mathematics: Solve And Win by Nobody: 7:18pm On Dec 15, 2017 |
freemandgenius: thanks...... |
Re: Mathematics: Solve And Win by thankyouJesus(m): 11:12pm On Dec 15, 2017 |
freemandgenius:Smiles.... |
Re: Mathematics: Solve And Win by Nobody: 4:18pm On Dec 27, 2017 |
freemandgenius: Christmas has passed and yet you did not fulfil your promise. I hope you know Promise is a debt? |
Re: Mathematics: Solve And Win by afo7219: 8:16pm On Dec 27, 2017 |
kelvinreality:pls tell d guy,I'm sure he doesn't |
Re: Mathematics: Solve And Win by efficiencie(m): 5:19pm On Dec 28, 2017 |
thankyouJesus: your solution method is not a generalization as you will not arrive at the same answer if you were to change the interval [x n-x] where n=8...will you answer hold if the interval were [x n-x] where n<8 or n>8? |
Re: Mathematics: Solve And Win by thankyouJesus(m): 11:33pm On Dec 29, 2017 |
efficiencie:Smiles....... You may need to read up the theorem sir. Instead of going that length..... I will appreciate an example of an interval where it fails. |
Re: Mathematics: Solve And Win by efficiencie(m): 10:57pm On Dec 30, 2017 |
thankyouJesus: Read my post well...I gave you a general set of intervals that will not provide you with a solution! I said will your answer hold if the interval were [x n-x] where n<8 or n>8? |
Re: Mathematics: Solve And Win by thankyouJesus(m): 8:26pm On Jan 01, 2018 |
efficiencie:Picking of interval is not random as you may think..... I'm working based on intermediate theorem.. .... Let's assume I don't understand you...... Could you please give an interval to assert your point. This is what I pick from your statement..... Let's assume n is 7..... I will be working with [4,7-4] = [3,4] right? |
Re: Mathematics: Solve And Win by thankyouJesus(m): 8:27pm On Jan 01, 2018 |
. |
Re: Mathematics: Solve And Win by efficiencie(m): 11:07am On Jan 03, 2018 |
thankyouJesus: Yes sir! |
Re: Mathematics: Solve And Win by thankyouJesus(m): 5:43am On Jan 04, 2018 |
efficiencie:Smiles..... Your interval wouldn't satisfy the mid value theorem I quoted because there does not exist a point that satisfies f(a) < 0 and f(b) > 0 totally. |
Re: Mathematics: Solve And Win by efficiencie(m): 1:19pm On Jan 04, 2018 |
thankyouJesus: Sir just agree that your method is not a generalization. if a=3 and b=6 the condition f(3)<0 and f(6)>0 will be satisfied but the image of the mid-point f(4.5) is non-zero. Your solution begs the question; how did you determine the limits 3 and 4? Did you determine it by sheer guess work or by some mathematical reasoning you did not include in your solution? |
Re: Mathematics: Solve And Win by thankyouJesus(m): 7:19pm On Jan 04, 2018 |
efficiencie: |
Re: Mathematics: Solve And Win by thankyouJesus(m): 7:23pm On Jan 04, 2018 |
efficiencie:Smiles.... I really wish I can explain the theorem to you.. .. Check out mid value theorem and bisection method on any good Numerical Analysis textbook.. .. Shalom.. . I need to do more iteration using your interval.. .. To your question.. .. It works for all.. . Permit me to ask sir.. . Do you know and understand bisection method and mid value theorem? |
Re: Mathematics: Solve And Win by efficiencie(m): 6:38am On Jan 05, 2018 |
thankyouJesus: Sir, I am not challenging the veracity of the theorem I am merely showing you that your solution is not a generalization. Your choice of 3 and 5 as the bounds in your interval was either by mere inspection or sheer guess and not based on mathematical reasoning. Nevertheless I may be wrong so tell us how you arrived at the use of 3 and 5 as the bounds of the interval you used. In addition, your interval is not unique as there is an infinite set of intervals that will satisfy the theorem above and yield the solution x=4 for the problem f(x)=2x - 4x where f(x)=0 [because by inspection, the interval [x n-x] where n=8 and x<4 will always yield your solution according to your stated theorem.] |
Re: Mathematics: Solve And Win by thankyouJesus(m): 9:58am On Jan 05, 2018 |
efficiencie:Smiles..... Check out any good Numerical Analysis textbook sir.. .. I ask again.. ..do you know and understand bisection method and mid value theorem sir? |
Re: Mathematics: Solve And Win by efficiencie(m): 11:48am On Jan 05, 2018 |
thankyouJesus: sir, mathematics is a lovely discipline...I do not have to be a professor of mathematics to know that there is a flaw in your mathematical reasoning. My simple question to you is; HOW DID YOU DETERMINE THE INTERVAL [3 5]? WAS IT BY INSPECTION (Anyone could do that) OR BY SOME MATHEMATICAL REASONING (which you did not specify in your solution). |
Re: Mathematics: Solve And Win by Timology55: 11:55am On Jan 05, 2018 |
freemandgenius: Solu. 2^x =4x Divide through by "4" 2^x/4 =4x/4 2^x/2^2=x 2^(x-2)=x......law of indices The same as: (1+1)^(x-2)=x Using Binomial theorem: (1+a)^n=1+an+n(n-1)a^2/2! +...... Where a=1 and n=x-2 Substituting, we gat: 1+(x-2)+(x-2)(x-2-1)/2!=x 1+x-2 +(x-2)(x-3)/2=x 1+x-2 +(x^2-5x+6)/2=x Multiply through by "2" 2+2x-4+x^2-5x+6)=2x Simplifying the equation x^2-5x +4=0.......quadratic equation Factorize the quadratic equation X^2-4x-x+4=0 (x^2 -4x)-(x-4)=0 x(x-4)-1(x-4)=0 (x-4)(x-1)=0 x=4 or 1 Checking: X=1 does satisfy the equation, hence it's an extraneous equation. Hence, valid answer is x=4 X=4.....Q.E.D My gift |
Re: Mathematics: Solve And Win by Evangkatsoulis: 12:12pm On Jan 05, 2018 |
kelvinreality:wrong. After removing log it should have been 2^(x-2)=x. |
Re: Mathematics: Solve And Win by Evangkatsoulis: 12:35pm On Jan 05, 2018 |
Timology55:your binomial expansion isn't complete. Why did you stop at the third term? |
Re: Mathematics: Solve And Win by Timology55: 2:19pm On Jan 05, 2018 |
Evangkatsoulis: You can proceed to the next term based on choice. |
Re: Mathematics: Solve And Win by Nobody: 3:31pm On Jan 05, 2018 |
efficiencie: Haha Have you heard of numerical methods of solving algebraic and transcendental equations? Bisection, Newton Raphson, Method of False position, Iteration method e.t.c.? You will keep on iterating till the exact solution is found or a given epsilon value (allowed error) is reached. If you start with the open interval (3,6) like you want and using bisection method, you'd get (sorry, I won't show the workings because I can't type and can't upload any picture since I'm using opera mini) first itertate ( initial point) = 4.5 second iterate = 3.75 third iterate = 4.125 fourth iterate = 3.9375 fifth iterate = 4.03125 hope you see how this sequence is converging to 4? If you have a computer and MATLAB installed ,try running this problem using [ITER] If you have it saved as an m file and you'd see how the technique works. Are you still in secondary school? cc efficiencie thankyoujesus 1 Like |
Re: Mathematics: Solve And Win by thankyouJesus(m): 6:27pm On Jan 05, 2018 |
efficiencie:If you have read about the theorem, your question about the interval would have been attended to.. .... It was by mathematical reasoning. ... The theorem is in the solution but your inability to recognize it has extended the solution too long. .... Please, check out the theorem before commenting on my solution again.. . I wouldn't respond to your mention again if it's based on the same issue. |
Re: Mathematics: Solve And Win by thankyouJesus(m): 6:30pm On Jan 05, 2018 |
Timology55:Smiles.. .. Your solution doesn't conform to Mathematics.. .. Why the use of 1+1 and not 5-3 or any operation that can yield 2? |
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