Factoring Algebraic Exponentials, An Algebraic Expressions With Unknown Exponents. 😒😒😒

[@bobwineland9936]

If you have X^X =X^1/X then we have the same base X. So then X = 1/X. Or X^2=1 with two solutions X=1, X=(-1). This seems to be a much faster way to solve. Thank you Jake for your dedication to our learning mathematics 😊

[@KulangLuderu]

Your are wonderful in giving solution I am like your way. Thanks Kulang

[@onlineMathsTV]

It's our pleasure to serve you and we are glad you gained some values from this video tutorial sir. We pledge to serve you better in the future. Much love for watching and commenting sir....💖💖💖💕💕

[@alicefosua9776]

I think , you can solve this by squaring both sides by x , and also taking log of both sides. By the thank you very much, keep up your good works.

[@opulence3222]

🧨👍👍👍

[@jiaotang9505]

Isn't it that from the original equation you get x=1/x based on law of exponents? Then from there you have x^2=1, which means either x=1 or x=-1? That should be straightforward.

[@onlineMathsTV]

That gives only two solutions and it is ok too sir.

[@hardsg]

​@@onlineMathsTVno zero can not be a solution 1/0 is undefined...so correct it

[@hardsg]

​@@onlineMathsTVsorry sir i went to straight to the end that i did not see that u said undefined.

[@libardouribe7617]

Super.

[@onlineMathsTV]

Many thanks sir......🤸‍♂️🤸‍♂️🤸‍♂️

[@baawabaawa393]

Equate the base form start, x=+-1

[@onlineMathsTV]

👍👍👍

[@lzuluaga6064]

Divide por un término y luego iguala exponentes, factoriza y listo.

[@onlineMathsTV]

Bravo 👍👍👍

[@FractAlkemist]

My Python equation solver (Genetic Algorithm) gives two values to solve the equation: x = -1 and x = +1. Zero is not valid as you get divide by zero error. Negative values for x (other than (-1)) give IMAGINARY numbers! Positive values for x (other than (+1)) give real numbers not much different from the input (x).

[@onlineMathsTV]

Zero is extraneous here. Thanks for the keen observation sir. Respect ....👍👍👍

[@comdo777]

asnwer=1x

[@lumionne0]

can't we just go with x = 1/x since both bases are the same on both sides?

[@onlineMathsTV]

Yes, but that will exclude the third solution

[@severusndingombaba9566]

There is no third solution. 0^0=0^(1/0) is not defined.

[@enki354]

I must be watching this on acid. It's true 0^0 and 1/0 are undefined; which means they can't be extraneous roots of anything. The answer to this would be the empty set. If I'm wrong please tell me why.

[@severusndingombaba9566]

0^0=1, 1/0 is indeed undefined

[@habeebalbarghothy6320]

لماذا لم تستخدم اللوغاريتم الطبيعي او العشري من البداية ؟ ام ان هدفك إطالة مدة الفيديو

[@severusndingombaba9566]

x^(1/x)=0 has no solution.

[@Frank-kx4hc]

In R, with base X and exponent p , this equation is equivalent to: X^p=1 • X=1 and p defined, • or X=-1 and p EVEN, • or p=0 and X0. See this trick here: kzbin.info/www/bejne/l3illmyFl9afraM

[@onlineMathsTV]

Nice one

[@s.h.munasingha2590]

X= 1 or X= -1

[@onlineMathsTV]

Bravo!!! 👍👍👍

[@Pascal-cy9sc]

x^(x-1/x)=1までは良かったのに、何故わざわざ両辺の対数を取る必要があるのですか？？？対数を取る条件は、指数部分を前に出す条件は、真数が正の実数つまり、x＞0の時で無いと一般には成り立たないですよ😅x^(x-1/x)=1なら、底の部分x=1になるか、指数部分x－1/x=0 又は底の部分x=－1の時に指数部分x-1/xが負も含めて偶数になるか、底の部分x=±iの時に、指数部分x-1/xが4の倍数になる場合なので、この全ての場合を求めれば、x=±1が解になります。

[@onlineMathsTV]

Bravo👍👍👍

[@MaurisonAgba]

Your approach is unnecessarily long

[@onlineMathsTV]

Noted sir. We will give a more concise approach in subsequent solutions. Much love ....💕💕💕💖

[@severusndingombaba9566]

...and incorrect

[@215055vv]

THERE IS ONLY ONE SOLUTION TO THIS EQUATION AND THAT IS X=1. YOU SHOULD NOT BE TEACHING.

[@onlineMathsTV]

Noted, I will obey your command and end this program sir. Your wish is my command master.

[@enki354]

Could you please explain why this is the case?

[@severusndingombaba9566]

There are in fact two solutions, 1 and -1. The "third solution x=0" is bullshit.