Well done. You can also do a base change to from x to x-1, which gives you the long division for "free". 1+1÷(x-1) becomes x÷(x-1), flip to get x+1÷(-x) all to the power of -x. Then switch back to original base.
Thank you so much, Professor! Both methods are equally wonderful, but still I still liked more the way of long division. All your lessons are a real pleasure! God bless you and your family!
Thank you sir. Your brain and imagination are fast and excellent Comparing both sides at first sight it seems to me x=23 or 24, but I could not solve it.. After your explanation it turns out x=-24. Amazing.
It is necessary to show that there's only a single solution. This can be achieved with a quick plot of the function on the LHS. The domain of the function is x>0 or x0, the function is always above the y=e line, and therefore doesn't intersect the value on the RHS of the equation. Similarly for x
You do an excellent job of walking thru all your manipulations. However I wish you would try to explain WHY you chose those particular manipulations, especially at the outset. They seem to come out of nowhere.
Deriving the answer with a variant of the formula is great. but I don't know how to indicate that there is no solution other than x=-24. What should I do?
It still bothers me sometimes though: where was the mathematical intuition coming from the way you did the first approach? It wasn't at all clear you'd come out with such a nice solution, doing what you did; it might have been a rabbit hole instead.
But u also need to check if there are other solutions for the equation. If we take x^(1/x)=2^(1/2). x=1/2 is a solution, that's obvious. But if u plug x=1/4 into the equation, u will find out that it's also a solution. Solving an equation means finding all of the solutions or proving there aren't any
@@Icewallocumm No, I am just pointing out the cool thing about what the value of x is! If we had to take |x|, then we are taking |-24|, then it is what letter in the alphabet it needs to be.
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Both methods marvellous. Your way of explanation to minutest detail is just amazing. Thank you Sir
Thanks and welcome
Glad to hear that! Cheers!
You are awesome, Niru. Keep it up 😀
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@@PreMath what would happen if we solve by taking log to both sides
Well done. You can also do a base change to from x to x-1, which gives you the long division for "free". 1+1÷(x-1) becomes x÷(x-1), flip to get x+1÷(-x) all to the power of -x. Then switch back to original base.
Excellent
Thank you so much, Professor! Both methods are equally wonderful, but still I still liked more the way of long division. All your lessons are a real pleasure! God bless you and your family!
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solutions are very well explained, love this exponential question, thanks for sharing
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Thank you sir. Your brain and imagination are fast and excellent Comparing both sides at first sight it seems to me x=23 or 24, but I could not solve it.. After your explanation it turns out x=-24. Amazing.
amazing ...ruclips.net/video/Ul1IaoZagOo/видео.html
It is necessary to show that there's only a single solution. This can be achieved with a quick plot of the function on the LHS. The domain of the function is x>0 or x0, the function is always above the y=e line, and therefore doesn't intersect the value on the RHS of the equation.
Similarly for x
Thanks sir for helping me and understanding me alot of concept 👍🏼
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I enjoyed both the clever manipulations. Thank you
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Way of teaching is very excellent
In the second method instead of dividing x by x+1 add +1 and _1 to the numerator we can get x+1-1/x+1= x+1/x+1-1/x+1
Eye Opening MIND GYM. Thank You so much
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The first method is easier and less time. Thank you for your work
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You do an excellent job of walking thru all your manipulations. However I wish you would try to explain WHY you chose those particular manipulations, especially at the outset. They seem to come out of nowhere.
amazing ...ruclips.net/video/Ul1IaoZagOo/видео.html
Deriving the answer with a variant of the formula is great. but I don't know how to indicate that there is no solution other than x=-24. What should I do?
really great! I'm missing how you demonstrate that there is only 1 solution?
I think because it is a kind of linear equation.
It still bothers me sometimes though: where was the mathematical intuition coming from the way you did the first approach? It wasn't at all clear you'd come out with such a nice solution, doing what you did; it might have been a rabbit hole instead.
thank you sir great methods
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Thnks a lot i needed such type of question
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Sharing friend 👍
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Thanks for video. Good luck sir!!!!!!!!
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Great idea
Nice solution
Thank you sir again
Always welcome, Hamad
Thank you for your feedback! Cheers!
You are awesome. Keep it up 😀
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Sir What is the software or equipment for doing this lectures?
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Amazing 👍
Thanks for sharing😊
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Very nice 👌
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But u also need to check if there are other solutions for the equation. If we take x^(1/x)=2^(1/2). x=1/2 is a solution, that's obvious. But if u plug x=1/4 into the equation, u will find out that it's also a solution. Solving an equation means finding all of the solutions or proving there aren't any
Where is the proof that there is no other solutions except -24 . There should be a positive root too somewhere between 22 and 23
Amazing 🔥
so nice exam , I try to learn more about this.
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LUAR BIASA !!!
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great solutions
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thx 4 the study
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아주 신빡하네요? 감사합니다^^
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Wow, amaze!
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Excellent
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Great manipulation 👍
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X^x = 4^x+16
Can you solve this plss
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Thank you sir
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Thanks
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Sir, are you Indian origin?
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شكرا
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Thanks sir
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espectacular
Unfortunately, you haven't proven there's only one solution
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4:12 YO! "x" is actually the 24th letter in the alphabet!!! But yeah, it's NEGATIVE, that is literally the only difference!
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Depends on what alphabet
@@Icewallocumm No, I am just pointing out the cool thing about what the value of x is! If we had to take |x|, then we are taking |-24|, then it is what letter in the alphabet it needs to be.
Nice one #mathmarvelasmr
Both methods are slightly similar
Still need to show that there are no other solutions
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cool
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神奇
You are manipulating numbers not calculating!