In todays video, I will be teaching you how to solve an interesting problem. Make sure to like, subscribe, and also comment any questions or video ideas you may have relating to math!
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ln3 is also multi-valued (in the complex world) . So there are more solutions.
You take log in this case not natural log!
U could just take the complex logarithm and it would have worked
"No real solutions" Job done. No need for further explanation. X^Y =/= Y * X.
1^x (where x is any value) =1.
Sorry, but I have to take issue with a few things in this video.
First, the math. I think when talking about complex logarithms, it's very important to invoke the idea of a branch cut. This is kind of shown by allowing for any nonzero integer value of k, but its not quite the same time. On that note, if I raise 1 to the power of (log(3) * i / (2 pi)), then I get 3^n where n is any integer, including 0. This resolves the problem that 1^x is 1 for any value of x. The true solution of e^(log(3)*i / (2 pi)) includes 1. This is really a result of the branch cuts. No need for k.
Second, and this is a personal pet peeve, it's pronounced "OY-ler," not "YOU-ler." I know it's confusing because we say "YOU-clid" and not "OY-clid." This is becaue Euclid is a Greek name, and Euler is a German name, so the pronunciations are entirely different. Also, for some reason, you wrote "Eurler" for the vid, with an r thrown in there.
I hope that you will consider these points as you continue to make content. Good luck!
Wolfram Alpha says if you plug the solution in for x, the result is 1.
I think he just divided both sides by zero
The world is correct. It was false when you posted it last time (https://www.youtube.com/watch?v=uSy-cmOigeY) and nothing has changed. There no real solutions and no complex ones, either. Please stop.
Stopped watching as soon as you spelled Euler as "Eurler".