Solving Exponential Equation With Radicals | Japanese Olympiad Math Question | Mathematics.

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In solving this Olympiad Math Exponential Equation with radicals, I will guide you on how to solve for the roots using a different approach different from the normal one you know.
In this Japanese Olympiad question, you will also learn how to handle the radicals with easy, formulate quadratic equation from the radical equation, substitute and factorize quadratic equation with easy.
I will lead you on how to use the natural logarithm to solve exponential equations.
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#matholympiad #exponential #radical #maths #mathchallenge #mathematics #math #mathtricks #olympiadpreparation #olympiads #solutions #mathskills #learningmaths #learningmathematics #simplification_with_tricks #simplification_tricks

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29 сен 2024

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Комментарии : 89

@teacherheng1688 10 месяцев назад

❤

@vansf3433 9 месяцев назад

It seems that you like solving children' s math-probs 3^x - 4^x = sqrt(14^x -16^x). Notice that the expression inside the radical can not be negative, but 14^x < 16^x ---> 14^x - 16^x will always be negative. There is only 1 way to neutralise the negative result is to make the expression= O. since any value taken to pwer of 0 will become 1. If x = 0, 24^0 -16^0 = 1 - 1 = 0 Checking whether x = 0 the solution: 3^0 - 4^0 = sqrt(14^0 - 16^ 0) 1 -1 = sqrt(1 - 1) 0 = 0. Hence, x = 0 is the solution We're done

@onlineMathsTV 9 месяцев назад

Ok sir, thanks for dropping this sir. We learn everyday from the best brains all around the globe and we sincerely believe you are one of these rare genius in mathematics. Nice to have you here sir, You are most welcome master.

@M.Davit613 Год назад

I solved the exercise in 2 minutes․ x

@onlineMathsTV Год назад

Bravo👍👍👍 You the master👌👌👌

@M.Davit613 Год назад

@@onlineMathsTV Thank U

@youncheolshin6304 Год назад

how about 0 or 1/{ log2 (3) - 2}

@onlineMathsTV Год назад

Thanks for the encouragement sir. We love you for watching and commenting sir. Much love 💕💕💖💖

@tunneloflight 8 месяцев назад

This also has the advantage that many calculators natively perform lg2, so x = 1 / (lg2(3) -2) is trivial to calculate. In RPN: 3 ; lg2 ; 2 ; - ; 1/x. {five keystrokes}

@marjaentrich7121 Год назад

Выражение под корнем должно быть не меньше нуля. Те, когда возаодили корень в квадрат, должны были получить модуль и нужно рассмотреть 2 случая

@moulikraina2186 Год назад

Can u give more questions like this?As the question was amazing and also the way to explain .i enjoyed ur explanation

@onlineMathsTV Год назад

We are glad you enjoyed and gained something valuable from this video. Sure, we can make more of this sir. Thanks for the request. Much love 💖💖💖

@BN-hy1nd 11 месяцев назад

Hmm, I should try a graphical solution method without drawing a proper graph Sketch a graph of graph of y = 3^x -4^x . y = (12^x -16^x)^0.5 when x = 0, y=0, certainly. y will always be +ve when x is -ve. When x is positive will generate complex numbers so, by inspection, both graphs meet at x=0 and y=0 Then try x = -1, -2 and -3 ; gradually the difference in y values get smaller and smaller In an exam, this sort of question requires an approximate answer for the second value

@ΔιονύσηςΤ-π5ρ Год назад

I firmly believe that either we should have restrictions for the solutions of the equation or, at least, if we ommit the restrictions we should check the solutions before we accept them.

@onlineMathsTV Год назад

Thanks for this wonderful comment sir. I have checked the two solutions and they are correct.

@اممدنحمظ Год назад

تمرين جميل جيد . شرح واضح مرتب . شكرا جزيلا لكم والله يحفظكم ويرعاكم ويحميكم جميعا . تحياتنا لكم من غزة فلسطين

@onlineMathsTV Год назад

Many thanks to you for finding our videos very fascinating and thank you for your wonderful words of encouragement all the time to us on this channel sir. All of us @Onlinemathstv love you sir. Much love from everyone of us @onlinemathstv to you, your family and all the people of Gaza, Palestine ...💕💕💕❤️❤️💖💖

@youncheolshin6304 Год назад

if you put 3^x =a, 4^x=b you can rewrite the question as this : a-b= root( ab-b^2) and square each side that can be (a-b)^2 = ab-b^2 ; a^2 - 2ab + b^2 = ab-b^2 ; a^2 - 3ab + b^2 = 0 ; (a-b) (a-2b) =0 ; a-b=0 or a-2b=0 ; a=b or a=2b ; 3^x= 4^x or 3^x = 2* 4^x ; its more simple what do you think?

@onlineMathsTV Год назад

Very concise sir. It is a welcome approach too. Nice work and we have learnt something new from your comment. Thanks for watching and dropping this comment too. Much respect and love to you sir...🙏🙏💕💕💕

@유도겸-i2i Год назад

빙빙 돌아가며 풀이해 지친다.. 무조건 자연로그로만 푸니 듣기가 힘듬

@vansf3433 9 месяцев назад

You don't have to copy all such lengthy steps of human -invented motions of algebra to arrive at the correct answer Again, logical reasoning can help you solve all sorts of problems, but not copying such lengthy formulas and steps, like a photocopying machine

@onlineMathsTV 9 месяцев назад

Noted and thanks sir.

@albinonhabanga8066 Год назад

I think it's very important to check first the existence conditions of some functions, as this square root, to detect non valid solutions or include in your solving Anyhow you are a beast 😎

@petermak3980 Год назад

You must set 3^x--4^x>=0 ...... x

@onlineMathsTV Год назад

noted sir. Thanks master.🙏🙏🙏

@loveharshvardhan4259 11 месяцев назад

Only one to notice. Hats off

@sobolzeev Год назад

I wonder who is meant as the audience of this piece. A general mediocre pupil will not get even this long and overworded explanation. A bit developed one (1) does not need 2/3 of this wording, (2) guesses x=0 is a solution in the first 30 seconds, by substitution, (3) since a square root from a negative number is not real, gets any other root is negative. Finaly, 3^x = 4^(x+1/2) can be trivially solved with much less wording.

@FractAlkemist Год назад

I tried my Genetic Algorithm with this; 'x' must be a negative number, and it needn't be an integer. There seems to be no real solution, the greater the (negative) number, the closer it gets. I scanned from 0-> -500 and the best I got was: X = -481.58408788993336 Left side evaluates to: 1.6826575283911937e-230 Right side evaluates to: zero (probably not real zero, the computer just doesn't display such a small number) Difference = 1.6826575283911937e-230 , effectively solving the equation (for engineers, not theoreticians!) (plus overflow errors and other Python squawking) Maybe I should watch the video ...... .

@onlineMathsTV Год назад

Smiles....nice work from you boss. But most times AI fails to give the actual result to a mathematical challenge. I believe you have watched the video sir. Did you agree with the approach I applied here? I made a video on a similar challenge with a different approach. Below is the link to that video, you can as well flip through it to check it out if you don't mind sir. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-0cWjl5616pQ.html And do not hesitate to make corrections where necessary because we are here to also learn from the best brains like you all around the world. Thanking in advance boss!!! Respect!!! 👍👍👍 Much love....❤️❤️

@vicferrmat4492 Год назад

Do you mean "generic" algorithm?

@HelenBlackG-xn9hf 4 месяца назад

🎉🎉❤❤❤

@DilaverHamzayeva-fs6fg 6 месяцев назад

🤎

@ChristelleHilaire-lb6pu Год назад

×=-3

@РавильГарифуллин-щ5ж Месяц назад

Ответ--6

@sans1331 Год назад

3^x-4^x=sqrt(12^x-16^x) y=3^x-4^x y=sqrty*(sqrt4^x) =sqrty*2^x divide both sides by 2^x 1.5^x-2^x=sqrty=y/2^x sqrty=y/2^x 2^x=y/sqrty=sqrty square both sides y=4^x=3^x-4^x +4^x both sides 2(4^x)=4^(x+0.5)=3^x z=ln4/ln3 [3^z=4] (3^z)^(x+.5)=3^x x=zx+0.5z *x both sides x^2=zx^2+.5zx -x^2 both sides (z-1)x^2+0.5zx=0 [1 rough quadratic formula later] x=(-0.5(ln4/ln3))/((ln4/ln3)-1) =-ln4/((2ln3)((ln4/ln3)-1) (2ln3)((ln4/ln3)-1)=((2ln3*ln4)/ln3)-2ln3 =2ln4-2ln3 =>x=-ln4/(2(ln4-ln3)) …and also x=0. edit: oh wow, different fractions yet the same constant

@onlineMathsTV Год назад

Wonderful and unique move. You are good at it sir, you the master here. Respect👌👌👌

@hogec_enlightenmentarena6975 Год назад

Nice 👍

@onlineMathsTV Год назад

Thanks sir.

@MeinhartKöster Год назад

thank you very much, i suggest that the value of zero for u should be rejected, for otherwise the division by ( 3 px - 4 px) being equal to zero would not work

@onlineMathsTV Год назад

But 3 px - 4 px (i.e 1-1) will give us zero, which implies LHS = RHS. What do you think sir?

@AloneStroller Год назад

I disagree with x2 solition - it is superfluous as we should use straight definition of logarithm: X2=log(3/4)2. log(a)b.

@onlineMathsTV Год назад

not too clear with your point here sir.

@MunaCabdulaahi-z2e 10 месяцев назад

hope see you again My teacher thanks for everthing

@Bertin-q3y 8 месяцев назад

X=0

@onlineMathsTV 8 месяцев назад

Correct boss, but that is just one of the solutions. Thanks for stopping by sir. Much love.

@SASS-yp8gu 11 месяцев назад

X не может быть равен "0", так как -1 не равно sqrt(-1)

@douglasjunior5062 Год назад

Eu não fazia ideia de pra onde ir 😅😅 vídeo muito bom

@onlineMathsTV Год назад

😍😍😍 funny you sir. Coming here means you will definitely know where to go next time you come across any mathematical challenge/problem as u consistently visit OnlinemathsTV channel. Much love....💖💖💖

@loveharshvardhan4259 11 месяцев назад

In this video, the respected teacher is attempting to divide by zero, the value for which remains undefined and unknown. Thereby, his method is wrong.

@onlineMathsTV 11 месяцев назад

Sir, are you of the opinion that zero as a root to this math challenge is wrong? Kindly do the simple substitution and check if an undefined expression will emerge in this math challenge sir. Thanking you for a positive response in advance.

@nasrullahhusnan2289 11 месяцев назад

I think there is no division by zero. In [(3^x)-(4^x)]²=(4^x)[(3^x)-(4^x)] the teacher didn't divide the equation by (3^x)-(4^x), rather he let (3^x)-(4^x)=u and then move all terms to one side. Directly moving all terms to one side follow by factorizing we get [(3^x)-(4^x)][{(3^x)-(4^x)}-(4^x)]=0 [(3^x)-(4^x)][(3^x)-2(4^x)]=0 Hence: • (3^x)-(4^x)=0 --> x=0 • (3^x)-2(4^x)=0 --> (¾)^x=2 NO DIVISION BY ZERO

@venky3867 Год назад

I'm proud that I could do this in my mind

@charlesmitchell5841 Год назад

Good problem. Good explanation. Thanks for the video lesson!

@onlineMathsTV Год назад

Thanks for the encouragement sir. And thanks for watching our contents sir. Much love❤️❤️💕💕💕

@s.h.munasingha2590 Год назад

,X= log( 3/4 ) 2

@syedmdabid7191 Год назад

What's is the meaning of Wn( 2) ?????

@brightjovanny 11 месяцев назад

Wn(z) is generally called the Lambert W function (or omega function or productlog) where the subscript n (an integer) represents the principal, positive or negative branch of the function with n = 0 being the principal branch. The Lambert W function is the inverse of the function: f(w) = we^w where w is any complex number and e^w is the exponential function. The function can also be written as: LambertW(n,z) ProductLog(n,z)

@JohanNgoko 11 месяцев назад

I already see 0 as solution 😅

@himnishdhiman1370 7 месяцев назад

Yeah but thats only one solution!!

@danielfranca1939 Год назад

Great explanation. This is lovely sir.

@onlineMathsTV Год назад

Thanks @Daniel Franca Love you...💖💖💕💕

@mahinofficial4671 Год назад

If we use log instead of using ln ,then what will happen

@onlineMathsTV Год назад

same result sir.

@faithlesshound5621 11 месяцев назад

Using logs to the base of 10, we can fill in the numbers (the logarithms of 2, 3 and 4, which are 0.3010, 0.4771 and 0.6020) from memory and then calculate the quotient by hand. I don't have natural logs in memory.

@StephieJoseph-io3wt Год назад

Thanks for making this video sir.

@onlineMathsTV Год назад

You are welcome always ma. Love you...❤️❤️💕💕

@johnwren6138 Год назад

Easier to go m log7=log70

@onlineMathsTV Год назад

Bravo 👍👍👍 You the best sir.

@ilyashick3178 Год назад

ln 1 is equal 0 so x1=0

@onlineMathsTV Год назад

Yap

@sudhakaranpillai9623 Год назад

In case 1,there is no need to go for' ln' because raised to the power 0 only gives 1

@onlineMathsTV Год назад

Noted sir.

@sepehrarkani6689 Год назад

Excellent videos. Greatly appreciated!

@onlineMathsTV Год назад

Glad it was helpful and thank you for appreciating our little effort sir. This is encouraging. Much love💕💕💕

@sepehrarkani6689 Год назад

@@onlineMathsTV you're very welcome 👍

@MathsTuitionBangla Год назад

Hello students

@onlineMathsTV Год назад

Hi master!!! Anything for the student/s? We are at your service as your wish is our command sir.

@abhijitgangopadhyay8962 Год назад

Thank you Sir

@onlineMathsTV Год назад

You are most welcome sir, and thanks for watching our content sir. Much love 💖💖💕💕

@shoshosalah3447 Год назад

X1=0 X2~ -2.41

@onlineMathsTV Год назад

Bravo 👍👍👍 You the best sir.

@desirekouame3946 Год назад

Congrats,bro !

@onlineMathsTV Год назад

Many thanks to you for encouraging us on what we are doing sir. Respect...👍👍

@F.S.L.C. Год назад

WOW - THANK YOU.

@onlineMathsTV Год назад

You're very welcome sir. We are glad you gained some values from this tutorial sir.

@honey-qqq Год назад

🙏

@onlineMathsTV Год назад

Thanks sir for you comment. It is a symbol but a big symbol of encouragement to us sir. We are glad that you gained some values from our little effort and we promise to do more effective work here in order not to disappoint you and others who believe even in our little beginning. We love you sir.❤️❤️💖💖💕💕💕