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

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

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

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

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

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

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

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.

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

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.

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

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

That is normal grade 10 math question in Asian countries.

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

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

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.

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?

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.

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

The final equation looks more complicated than the original equation.

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

Your speaking very bad

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

I not interested your math solve

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 🎉🎉🎉🎉❤

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

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

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

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

*This is an absolutely rubbish, it's not the correct solution of the problem*

You call it a salvation?

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

This answer shouldn't be accepted.Just think a little ;what is solution actually?It means simplyfying the complex equations.But watching your answer anyone would say that the answer is more complex than the question.

This is not an Olympiad question. This is very basic 8th grade algebra. Stop giving misleading names to your posts!

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

😑😑😑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.

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

Que demora, ganhou até do Marcos Aba na lentidão, repetiu 8x cada coisa de forma desnecessária, assisti na velocidade 2x e me tapei de nojo da lentidão.

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

16 yo (10 class) vietnamese student could solve this with logarit under 1 min

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)

The solution is not true. If you want to keep an equation true, you can divide both sides to same value ( or number). And also the solution is too long.

Если это у них олимпиадная задача, то чем они вообще в школе занимаются?

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

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.

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

Совершенно дикое решение. И ещё и логарифм без основания!

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

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

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

Молодец итого получается х =1,1/3

А можна ще більше спростити: х = log5/(log6 - log5) - 5

1:40 and to 2:25 i don't understand

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

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

It is not a trick

I always bet on the exponent.

30 sec. Question made it for 6 min long

The Latex equation on title is wrong.

Just take the ln for both sides from the beginning

Не смогла досмотреть до конца - очень нудно.

hmmm? just take log in first eq.

Explanation is very long and boring.

this looks like a regular exercise from school

Kejauhan jalannya keburu abis nasiny

Too long process... It could end in 3 steps

Buen problema! Me suscrivo

5 won't do x it does b 5b -3 +3.4 =5th of 16

Just take log or ln from the beginning

Every simple and easy to understand explanation

The solution hasn't finished yet!

Где основание у логарифма

You said trick, I don't think so.

This is not a math olympiad question

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)

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

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.

Smkh me nhi aa rha please 1 video bnao

Easy taking log both sides

no se puede cumplir la igualdad

What. No. No. In. Korea. A step

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

The answer is x = 3,8258

how long is that paper

Extremely complicated

A two liner problem !

Trick? I took the log on both sides and arrived at the same. Nothing special

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)

I give up math after this video. 😊

Too simple for olympiad

Log siiis res to pawer fave log siis

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.

كوس اكس ؤس = 1

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

The camera is so close ,

Ez math

Pick from option 😂

log5=1-log2 log6=log2+log3

If X = 1... solved!!

When teacher told you each steps contain marks . 😅😂

The answer is 3.8274691 Done without logarithmic 🥲