My brain immediately changed the 1 to 3^0 and I had the real solutions. I wouldn't have been able to do that a month ago. As always, thank you for leveling up my math skills.
Are there no other branches of "ln 3" that we need to consider? How about other branches of the square root operation at the end? (I don't know how to tell if such things matter.)
Since the exponent is equal to 1, there are three cases: power is 0, base is -1 and power is even, and base is 1. Since we know the base is 3, the only possible way to find the real solutions is to set the power to 0. We have x^2-2x=0, solve by factoring. x(x-2)=0 so the real solutions for x is x = 0, 2.
You're correct, but those are only the real solutions. The main purpose of this video is to find the complex solutions, since x²-2x=0 is the obvious solution and doesnt really make content for a whole video.
The complex solution to this exponential equation is obtained with complete precision, it is even indicated that when n=0 the only two trivial real solutions for the equation are obtained.
I accepted the challenge and set x = a + bi. The values for a and b are too long to try to type them here, but they are achievable within half a page of calculations.
My brain immediately changed the 1 to 3^0 and I had the real solutions. I wouldn't have been able to do that a month ago.
As always, thank you for leveling up my math skills.
My pleasure 🤩
You made life too complex😅
yep 😁
Yup...
X = 2
That is what I got...
Are there no other branches of "ln 3" that we need to consider? How about other branches of the square root operation at the end?
(I don't know how to tell if such things matter.)
0 and 2
Since the exponent is equal to 1, there are three cases: power is 0, base is -1 and power is even, and base is 1. Since we know the base is 3, the only possible way to find the real solutions is to set the power to 0. We have x^2-2x=0, solve by factoring. x(x-2)=0 so the real solutions for x is x = 0, 2.
You're correct, but those are only the real solutions. The main purpose of this video is to find the complex solutions, since x²-2x=0 is the obvious solution and doesnt really make content for a whole video.
@@selimcalskan9442 but it’s a quadratic so isn’t there only 2 possible solutions ?
@@flam3guin114 its not a quadratic, its a nonstandard equation. You cant know x²-2x=0 because 0 is not the only value that makes 3^x equal to 1
Maza aa gayaa 😂
Translation: Had fun 😂
Nice - I got the same family of complex solutions. However, you forgot the real solutions: x=0 and x=2!
Those come up when you set n = 0 in the 2n(pi)i expression, which eliminates the imaginary part.
The complex solution to this exponential equation is obtained with complete precision, it is even indicated that when n=0 the only two trivial real solutions for the equation are obtained.
The real answers are immediate -- so the proof of your having found all real and complex solutions is really interesting.
Finding real solutions a lot easier
sure
I accepted the challenge and set x = a + bi. The values for a and b are too long to try to type them here, but they are achievable within half a page of calculations.
Wow! maybe share a picture you post on twitter or postlmg.cc/
@@SyberMath I tweeted it and @ed you.
Just imagine all the possibilities...
Problem: x +1 = 2, solve for x
Answer x = e^(2 n pi i), n is integer
I guess, if it doesn't say real numbers only... darn Euler
One simple solution, X^2-2X=0
then X=2.
x = 0 or 2
X^2-2x=0....x=0,x=2
x^2 - 2x = 0, etc. The upper case ex and the lower case ex are two different variables.
👍
Hello
Hi
Is it necessary to find the complex solution? In reality, students are not supposed to work out of them and no extra marks will be given. 🤔🤔🤔🤔🤔🤔
yes
0,2
You don't need to waste time trying to do complex numbers and all, but why not set this as 3^(x(x-2))=3^0. Therefore, x=0 and x=2.
Because he stated at the outset that he wanted to determine all possible solutions, including the complex ones.
@@jpolowin0 it's true and that's correct, but it's just to make things a lot simpler and save time.
Because he was trying to find out all the solutions
He was experimenting
exactly! Thanks