Math Olympiad Question 5^x+6=6^x+5 | This Is Best Trick | Beautiful Exponential Equation...

This video will teach you how to solve the given nice math olympiad exponential equation quickly with the Fast trick.
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[@silverodiete]

This is a long process. Just take log of both sides and solve the linear equation for x easily

[@olddog57]

The guy just misleads public calling this "Olympiad math". Besides, he doesn't solve equations well

[@gautamk4027]

​@@olddog57 well why dont you show your easy trick bot

[@kishoreahmed]

Even chat got did the same

[@ameerelshabrawy9905]

@@gautamk4027 why would he do that?

[@TakeAbackPak]

Exactly. Lately many of these are just nonsense!

[@mivanfernandes442]

Am I the only who came here because I couldn't mentally solve it after watching the thumbnail......

[@aka620]

Every simple and easy to understand explanation

[@pureffm]

Another method that avoids the complicated fraction at the end: 5^(x+6)=6^(x+5) 6 (5^(x+6))=6^(x+6) Let's assume X = x+6, the equation becomes: 6 (5^X)=6^X Log 6 + X Log 5 = X Log 6 X =Log 6 / (Log 6 - Log 5) x = X - 6 = Log 6 / (Log 6 - Log 5) - 6

[@larisamedovaya9097]

The final expression will look more simple, if you use as a base of algorithm (5); if you look for specific answer to use logarithmic Table, you can use base of 10 ,written ( lg) or base of “e” written (ln), otherwise, when you use abbriviation log, you should name the specific base.

[@darkobakula5190]

In my CS textbooks, lg is defined as binary logarithm and log is defined as log. ln is log of base e

[@larisamedovaya9097]

When I studied at school, junior college and university, we used lg for base 10, for e abbreviation ln

[@riki1578]

​@@larisamedovaya9097 well we used to take 10 for log and e for ln. As far I can remember we used to call ln as natural log.

[@BrunswickTchatchou]

I solve a similar equation in this vidéo.using two méthodes kzbin.info/www/bejne/rn3aonuHoZJ4b80

[@user-eo2ed7lr2n]

Здесь в принципе и делить нет необходимости. Сразу обе части логарифмируем, выносим степень за знак логарифма и получаем (x+6)ln5 = (x+5)ln6 Далее раскрываем скобки - xln5+6ln5 = xln6+5ln6 и переносим все с x в левую часть, а без x - в правую: xln5 - xln6 = 5ln6 - 6ln5. В левой части выносим x за скобки и получаем x(ln5-ln6) = 5ln6 - 6ln5 ну и делим обе части на ln5-ln6 и имеем тот же самый ответ

[@slavash9963]

При чём тут натуральные логарифмы? )

[@user-rh5rj9pf6v]

@@slavash9963 no difference what base of log. The expression is slightly better in case of base 5.

[@user-vi5fj8ov8m]

Это конечно, дно.

[@user-qq5kv6nd6h]

@@slavash9963 основание логарифма для решения не имеет значения, главное, чтобы оно везде одинаковое было. Можно взять по произвольному (тут в треде рекомендуют 5 для удобства), можно натуральный, можно десятичный - вообще без разницы, основание нужно только если хочется узнать окончательное число.

[@user-ne7pu8ib7y]

​@@slavash9963 когда степень неявная проще логарифмировать с помощью натурального логарифма

[@Psykolord1989]

Before watching: There is no integer that satisfies for this, because there is no integer x such that 5^x will be anything but 5 to some power. However, using rational numbers, we can get this. Start off taking log_5 of both sides. -> x+6 = (x+5)log_5(6). = (log_5(6))x + 5log_5(6). Move all the Xs to the right and the constants to the left... ->6-5log_5(6) = (log_5(6)-1) x X = (6-(5log_5(6)))/(log_5(6)-1). Most teachers will let you leave it in this form, or will let you use a calculator or log table. However, if you are faced with a multiple choice problem... Log_5(6) is going to be slightly more than 1 (since log_5(5)=1, and *much* less than 2 (log_5(25)=2. Bearing this in mind, 6-5log_5(6) is going to be a number between 0 and 1. Since we know the curve of a logarithm has a much steeper slope the closer to 0 you get, the difference 5log_5(6) and 5 should be surprisingly steep; we can assume (if we don't have a calculator!) that log_5(6) is something g like 1.1, maybe 1.15. This gives us a 6-5log_5(6) somewhere between 0.25 and 0.5. Log_5(6)-1 should also be a number between 0 and 1, but a much smaller number than 6-5log_5(6). If we take our 1.1 to 1.15 from above, then log_5(6)-1 is between 0.1 and 0.15. This means that (6-5log_5(6))/(log_5(6)-1) will be somewhere between 1.67 and 5. This ought to let you rule out most options on the test. With the use of a calculator and/or log tables (and possibly change of base formula), you should come to approx. 3.82746912.

[@solomonwilliams9708]

If you really fool around with the solution, x = [ Log (base 6/5) 5 ] - 5

[@maths-pro-by-khan-sir]

*Yes Sir, you are 100% right*

[@vitorgarciabarros9873]

Yes, I was worried whem I saw the vídeo solution and wasn't what I foud.

[@fatianass8317]

well, i've found: x = log base 5/6 of 1/6

[@shovankumarbiswas2204]

Calculate the value x=log(5/6)^(7776/15625) Here 5/6 is base and 7776/15625 is the value of which power of that base

[@apgamerff4585]

Can u do’the power in a competitive where no calculator is not provided and less time live jee mains or advance sir

[@jacksonrodgers3892]

I feel like I have a much simpler way. The bases can be made the same since 5 = 6^(log(6)^(5)) where the log is the power that 6 has to be raised to for it to be 5. Then the problem becomes 6^((log(6)^(5)) * (x+6)) = 6^(x+5) and since the bases are the same (log(6)^(5)) * (x+6) = x+5. Then evaluating the log it becomes .89824(x+6) = x+5 and using algebra the answer x=3.827 is found.

[@LovelyGil]

As a freshman highschool..... Man Idk how I understood this video... Well explained

[@club6525]

Assume 5^(x + 6) = 6^(x + 5). Thus, x * log(5) + 6 * log(5) = x * log(6) + 5 * log(6). Then, the equation can be rearranged as follows to solve for x: (1) x * log(5) + 6 * log(5) = x * log(6) + 5 * log(6) (2) x * log(5) - x * log(6) = 5 * log(6) - 6 * log(5) (3) x * (log(5) - log(6)) = 5 * log(6) - 6 * log(5) (4) x = (5 * log(6) - 6 * log(5))/(log(5) - log(6)) Then, simplify: (1) x = log(6^5/5^6)/log(5/6) (2) x = log(base 5/6)(7776/15625) Thus, x is approximately 3.82747

[@rohitvishwakarma1469]

I love the class sir.

[@BKKGarrett]

Much simpler way: 1. Take log of both sides and bring exponents to the front of the logs in ()'s. 2. Distribute the log 5 and log 6 to the terms in the ( )'s. 3. Bring terms with x's to the left of the = and other terms to the right. 4. Factor out the x from both terms on the left. 5. Divide both sides by the expression multiplied to the x's on the left. Finished.

[@muhammadmuwaffaqazmanali]

How that? Can I see??

[@RemnantRoad]

@@muhammadmuwaffaqazmanali Ok, here goes Take the log of both sides where log (a^b) = b log a : (x+6) log 5 = (x+5) log 6 Distribute: x log 5 + 6 log 5 = x log 6 + 5 log 6 Isolate x to one side: x log 5 - x log 6 = 5 log 6 - 6 log 5 Factor out X: x (log 5 - log 6) = 5 log 6 - 6 log 5 Isolate x: x = (5 log 6 - 6 log 5) / (log 5 - log 6)

[@muhammadmuwaffaqazmanali]

@@RemnantRoad Thanks bro 👍

[@BrunswickTchatchou]

I solve a similar equation in this vidéo.using two méthodes kzbin.info/www/bejne/rn3aonuHoZJ4b80

[@l.w.paradis2108]

Nice

[@heartlessdemonking1624]

His final answer was literally my 3rd step 😂😂😂

[@mohammadhassanakhlaqi526]

Exactly by taking log both side at the beginning .

[@heartlessdemonking1624]

​@@mohammadhassanakhlaqi526 exactly 💯💯

[@tutorchristabel]

thanks for a nice video

[@mathgist3706]

So nice of you

[@gleicejamb7368]

😂😂😂😂😂precisoooo desse professor a vida e inteira ,nem se fosse colocando acertaria pra fazer do fim pro começo,eu acertaria ,caiu no log🥲🤔🤔🙃🙃🙃🙃🙃🙃🥵🥵🥵🥵😃😘🥰🤟🙌

[@club6525]

xlog5 + 6log5 = xlog6 + 5log6 x(log5 - log6) = 5log6 - 6log5 x = (5log6 - 6log5)/(log5 - log6)

[@pureffm]

And the last step x = Log 6 / (Log 6 - Log 5) - 6

[@RonnyS.1900]

​@@pureffm please elaborate, how did you reach to this step ?

[@pureffm]

@@RonnyS.1900 This is what we get: x = ( 6log5 - 5log6)/(log6 - log5) x = [(log 6 - 6* (Log6 - Log5)]/(log6 - log5) x = Log 6 / (Log 6 - Log 5) - 6 It is simpler with a substitution method (see my other comment for that method)

[@JoseGomez-yg1yd]

Buen problema! Me suscrivo

[@mpniko]

Solve by linear equation or solve by taking log , Answer is x=3.82 No need to complicate that much

[@1234sidor]

It' not olimpic task, it's quite simple one for ordinary schoolchildren: take log first and then solve linear equation

[@lawless18]

very hard this one...thank you for resolution.

[@latashasanders]

thanks.

[@suparnadas3997]

Suppose x+6= y and x+5= z Then, 5^y = 6^z • we know, if we have 5 with any power it always have '5' number at last. {For eg. 5³= 125, 5⁴=625} •And, 6^ any number has number '6' at last.{6²=36, 6³=216} ✓ Hence, no whole number is possible to make 5^x+6 = 6^x+5 🎉🎉🎉🎉❤

[@chibuikendubisi7125]

Its helps me very well Thanks

[@mathgist3706]

Most welcome 😊

[@sans1331]

5^(x+6)=6^(x+5) ln both sides (x+6)ln5=(x+5)ln6 xln5+6ln5=xln6+5ln6 -xln6 and -6ln5 both sides xln5-xln6=(ln5-ln6)x=5ln6-6ln5 x=(5ln6-6ln5)/(ln5-ln6)

[@tunneloflight]

the answer cleans up further to (1 / (1-log(6)/log(5) ) - 5, where the logs can be to any base. If you choose base 5 it is ( 1 / (1- lg5(6)) -5

[@zplusacademy5718]

Hello sir ❤️🙏now m your friend forever ❤️🙏🙏 extremely beautiful steps in calculation of 🙏🙏

[@mohammadhassanakhlaqi526]

POV : you are an IIT aspirant and laughing at these questions

[@ariadnekalakou8302]

Easy but fun

[@farhadhasan2023]

I've another ans. Why don't you check this. X= (log (6/5) base 5) - 5)

[@josesszwec835]

Hi, professor. I've divided by 5 at the beginning. Calculation seems a bit easier then. Thanks!

[@evgenyzak2035]

Clever move!

[@BrunswickTchatchou]

I solve a similar equation in this vidéo.using two méthodes kzbin.info/www/bejne/rn3aonuHoZJ4b80

[@babaji1947]

The final equation looks more complicated than the original equation.

[@oliviertalon2277]

Trop longue comme démarche. Cet exercice peut être résolu en 30 secondes en prenant le log de chaque terme dès le début et c'est beaucoup plus simple avec moins de risque d'erreur.

[@alexwongly43]

Stp Tonton, donne nous un exemple !

[@user-sn5jp1mq9u]

IMHO, this exercise is very simple, not suited for the olympiad level. Really, it took me less than 1 minute to solve. Can you please, professor, propose more curious exercises?

[@mathgist3706]

Alright. Thank u

[@azamatkurmangaliyev6010]

this looks like a regular exercise from school

[@ameerelshabrawy9905]

Just take the ln for both sides from the beginning

[@dazeyareyare1728]

Ez math

[@VoteScientist]

I always bet on the exponent.

[@swapnilchattopadhyay3428]

Take either log base 6 or log base 5 and then solve. 4 step answer you will be getting all together

[@nikhilpatidar9338]

Last step me log ka base kya lagaoge

[@honesttruth8710]

That is normal grade 10 math question in Asian countries.

[@roger7341]

Keep it simple; take the natural log of both sides (x+6)ln5 = (x+5)ln6 Solve this linear equation for x.

[@entranceexamvideos]

I thought the answer is surprisingly exact or rational. But it is just common random given. Math olympiad question's mostly arrived with simplest possible answer.

[@toanphamvan8930]

✅

[@TechnocratSohail]

It is better to take log on both sides and solve easily..

[@Mrperfect007]

Easy taking log both sides

[@abhasmishra8169]

Is it possible that this equation does not have any solution for x because 5 to the power anything will give a number which has 5 at units place and 6 to the power any number will give number having 6 at its unit place and that can't be equalise.

[@abdellahmyouri3565]

❤❤❤

[@manuelsuarezcosta5737]

😮

[@mehdisafari5221]

Hello We can solve the problem : [5]^(X+5)*5=[6]^(x+5) Then invide to ÷(1/5): [5/6]^(x+5)=1/5 Will have: (x+5)Ln(5/6)=Ln(1/5) Then: divide the sides of the tie into: x+5= Log (1÷5) : (1÷6) Result: X=-5+Log 0.2 (5÷6)

[@bryxer7v7]

I don't know if you will see this or not but I want to know what I did wrong... 5^(x+6)=6^(x+5) log5^(x+6)=log6^(x+5) 5 5 x+6=log6^(x+5) => x=(x+5)log6-6 5 5 log6=y 5 x=(x+5)y-6 [x=xy+y5-6]divided by "x" => 0=y+(y5/x)-(6/x) => -y=(y5/x)-(6/x) multiplied by "x" => -yx=y5-6 then divide by "-y" => x=-5-(6/-y) => x=-5+6/y and finally : x=-5+6/(log6-log5)

[@jonasnamesemudika3151]

Just take log or ln from the beginning

[@chrizbg2438]

Hizo muchos pasos para algo muy sencillo..

[@sparshagrawal]

This can also be written as 25^(x+5)=6^(x+5) ??

[@qwang3118]

Taking log(.) first, then it becomes a linear equation in x. Solve it. No tricks here.

[@marklevin3236]

Take ln of both sides and we get a linear equation.

[@oboubiprince5429]

How please

[@i_love_pasta_and_purple4539]

how long is that paper

[@07Pietruszka1957]

Too complicated method at bigining; Better start with log[5^(x+6)]=log{6^(x+5)] ...(x+6)*log(5)=(x+5)*log(6) and now solve x

[@Ligatmarping]

This doesnt look as an olympiad problem. Even the starting rounds, they are easier but have some idea other than just a direct calculation.

[@eddiesamuel3721]

ln >>>>>>>

[@Abood-vq8ix]

Mashaa allah

[@Shiv-jq4sk]

U died by allah allah speaking , read and learn something in life😂😂

[@Abood-vq8ix]

@@Shiv-jq4sk You don't see what we do in islam There are many of Muslim scholars

[@subratmeher1854]

Solve this by without logarithms, then this is great Do that...

[@ayushgarg5901]

Please provide a quick solution

[@danielechegaray288]

3.83

[@victormeng1952]

I take logrithm on questions of this or similar pattern, it's become an instinction.

[@Shiv-jq4sk]

Can we take both side log to base 10

[@victormeng1952]

@@Shiv-jq4sk That's literally the same thing. cz log a b=lnb/lna. so there's fixed ratio between base10 and base e.

[@Shiv-jq4sk]

@@victormeng1952 if we take log base 10 both sides then after first step we have ,x+5 log 6 = x+6 log 5 and after the solution we have x=5 , is this is a correct method

[@victormeng1952]

@@Shiv-jq4sk correct method wrong calculation

[@Shiv-jq4sk]

@@victormeng1952 can you calculate

[@user-gu7fx8tm7i]

양변에 상용로그 붙여서 로그 성질 이용하면 10초컷인데요.대한민국 고1들은 암산으로 풀어요.

[@andychang9478]

log5=1-log2 log6=log2+log3

[@mohammedelhouari5091]

ok for the resolution but you are not able to write an equality when using fractions. Thanmks

[@mickinetsystems]

U could have started straight by taking log of both side straight away…Long process

[@ariadnekalakou8302]

I used ln

[@user-oc4bm5hr9x]

Could any 1 friends tell me how you divide by scientific calculator the below 100÷ 0.0000000000155 ?

[@T-Accounting]

By taking the natural logarith both sides X=3.827469

[@CCCompiler]

I confirm that you are not human giving that answer

[@fande1337]

what are the bases of those logs???

[@crispyboi7]

If ‘log’ is written with no base it is typically base 10, but technically doesn’t actually matter what base it is since you log both sides. could be e or any other number as long as they are all the same it will give the same answer👍

[@fande1337]

@@crispyboi7 thank you for the explanation

[@fande1337]

@@crispyboi7 but log with base 10 should be written as lg

[@toeithanakrit2234]

hmmm? just take log in first eq.

[@Lacostta2]

Mas nesse time 2:55 aqui já está resolvido sem precisar de log.

[@ilyashick3178]

x=ln6/(ln6 - ln5)

[@yadkurdish99]

Hi i just didn't understand the (division part) can someone explain please? thnx..

[@abeonthehill166]

Using paper and pen, copy the teachers method , stopping the video if needed and repeat doing the calculations as you progress ! Repetition is the key along with verification of your equation.

[@user-bf3wc6dj1b]

Молодец итого получается х =1,1/3

[@ajeethpandey]

A two liner problem !

[@rubenfregaville4772]

Nice explicación,clear for understanding all steps,regards from Buenos Aires Argentina,thanks

[@BrunoPessolani]

The answer is x = 3,8258

[@amarjityadav9335]

Smkh me nhi aa rha please 1 video bnao

[@Bcex_uMeJI_u_Bce_MaJIo]

You call it a salvation?

[@julioigliori7631]

A forma de escrever precisa ser revista Um pouco de estética vai bem

[@King-cf1yr]

I give up math after this video. 😊

[@mathgist3706]

Why? Math is sweet

[@ij_1243]

When teacher told you each steps contain marks . 😅😂

[@ruddyxmax]

The Latex equation on title is wrong.

[@leidioml]

Que resposta é essa moço ?

[@Myst-Blazeio]

😑😑😑and here i thought x will give a value instead of another equation to solve using the log table. He just overcomplicated the whole thing. It can be easily solved by taking log on both sides.

[@rohanafroz]

Is it just this question or math Olympiad really that easy?

[@marshallsmith8106]

He's making sound much more complicated than the actual problem.

[@doldary]

문제가 재미 있거나 신기한 풀이가 있나 기대 했는데...

[@jaytailor8884]

X tends to Infinity

[@hernancontreras-it4ol]

One crop circle was to built some bullshit table mat had me piss asf contour lmao why is the math hitting hard

[@short_clips074]

6

[@ZeynepCeylan-ho1ye]

Adam uzattikca uzatmış beynim gitti bu ne aslinda çok basit bir doru ama afam bence sirf havalı olsun diye uzatmış

[@user-og8yg1qr6s]

x=3.41

[@shyams9658]

3.827