Olympiad Math Question | Exponential Equation | Solve x^x = x^2

Olympiad Math Question are one of the tough, complex and sometimes confusing mathematics to solve.

But this can be disputed when you know the rules of mathematics.
In this video I will show you how to solve exponential of this kind quick with easy through the application of some mathematical laws.

Here, you will learn how to make use of the division law of indices and the power law of logarithm.

I will show you how to introduce or use natural logarithm in solving this kind of exponential equation in order to get the true value(s) of the variable in question.

I will also introduce you to the zero product property use in solving quadratic equations by factorization.

These and many more ideas to learn from this video and to get all of them, kindly stay till the end from the beginning of this video without skipping any part.

Also subscribe to this channel in order to get more and better knowledge in mathematics.

Happy watching

[nasrullahhusnan]

x^x=x² is an exponential equation.
As the base is the same, x, then the power must be equal --> x=2
As the power differ then the base is the same then x=1.

[flance]

I wanted to write "It is obvious! It's just 2, why do you do it all" and after that you showed that there is two solutions here. 1 is also is the answer.
Thank you from Russia

[fron]

If you cannot solve this within one or two seconds, then do not participate in math(s) competitions.

[alozin]

after you divided both sides by x^2, my thought process was if you have 2 integers a and b, we can write it as a^b=1 if a=1, which if we look back, we see a=x which equals 1. then I did it pretty much the same way you did it afterwords

[ultimatememe]

Everyone in the comments section is talking smack about how easy of a solution this was, but I think what he did was brilliant. He isn't trying to make it overly complicated for a wow factor, he's just trying to show how you can find the solution to this type of problem.

Sure most people can solve this in their heads immediately, but what if you're faced with a similar type of problem that you can't just solve in your head? I think he does a great job at explaining the general solution, and the fact that it's so simple makes learning the concept a lot easier.

[PowerBuffBoys]

Nice video. You got a new subscription.

[yurynovitskiy]

It seems more simple without dividing to take a ln :
xlnx=2lnx then xlnx-2lnx=0, then
(lnx)(x-2)=0 then x=2 or lnx=0 i.e.x=1

[leos.]

the solution he used is actually very well thought out, and honestly it's very well done, explains perfectly all the concepts behind this simple exercise, . congratulations

[dankhank]

Got this exact question on a math test, thank you for saving me lol

[sumitsarmah]

Thank you sir for both the solutions.
As when I solved it by comparing expontents(as base are same) I ended up finding only one solution (that is 2)
This video will be very helpful for these type of problems

[lukethompson]

Don't listen to the rude people, they don't understand that you are teaching how to find the solutions to problems that might have a harder exponent.

[soheilBTI]

Thanks man, its is good to learning this solution 🌹

[felipef]

Hello, thank you for your video, but I am confused at the explanation at 4:51. Would you kindly explain what you did there? Thanks in advance!

[fernandos.]

☺️ Excelent work. A big hug from Mexico 😊

[dearcath]

2:10 after this part, what if you rewrote 1 as x⁰ ? Then the base would be the same and you can work with the exponents to get x = 2.

[jakeswealthworld]

Thanks Jakes for the good work. You the best

[burlerevathi]

Good evening sir!
we can also do it in a simple way ! there are in exponential form if bases are equal then powers equal to each other so, x=2

[thelifeofibo]

Get log base x on both sides,
x = 2 ✅

[MK]

You could take it logically and say the bases are the same so x must be 2 or say x could be 1 because 1^1 = 1^2

[chuksnonso]

Great works. This is unique, thanks sir