An Exponential Equation with Logs | Surprising Results

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PLAYLISTS 🎵 :

[MohammadAhmad]

Thank you very much, a professional teacher who deserves all respect and appreciation

[luker.]

I can't seem to convince Wolfram Alpha to give me the complex solutions for log base 10. However it would give them for log base 2 and 3, which were an absolute mess.

[scottleung]

Interesting exploration of WA's answers!

[michaelbaum]

Wow, this complex solution is very interesting 👍

[XJWill]

I would like to know what you typed into Wolfram Alpha to get that set of solutions, because when I type :
complex solutions z^(Log(z)/Log(10)) = (sqrt(z))^Log(z)
or anything like that, it gives me a single solution, z = 1. Which, incidentally, agrees with my own computation, assuming everything is taken to be the principal branch (principal value) in the given equation. There are no complex solutions in the principal branch of the equation shown in the video. And since WA uses the principal branch, it should not have returned the solutions you showed.
By the way, I have commented repeatedly that your misapplication of exponentiation identities that are valid for positive-real-numbers but you apply them to complex-valued numbers, will get you into trouble eventually. Your answer in this video is incorrect. And (z^w)^p does NOT equal z^(w*p) in general for complex numbers (or even for some negative real numbers).

[ftorum]

Equastion with complex numbers (sinx)^3+(cosx)^3=2

[alextang]

x^log(x)=(sqrt(x))^ln(x)
Take ln both sides,


Therefore,
ln(x)=0 or log(x)=ln(x^(1/2))
case 1,
ln(x)=0
x=1 answer
case 2,
log(x)=ln(x^(1/2))
2log(x)=ln(x)
2log(x)=log(x)/log(e)
Therefore log(x)=0
x=1 answer
So, the answer is x=1 only. 😋😋😋😋😋😋

[lazizbeknomozov]

f(x+y)+f(x-y)=2f(x)cosy f(x)=? x, y€R plz help me