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7,310 Views • Jul 5, 2023 • Click to toggle off description
#Shorts #Math #Maths #PreMath #MathTricks #MathTrick #MathTrickHacks #MathHack #MathHack #short #Solve #FindSolutions
Find all solutions for the equation.
• CAN YOU FIND THE SOLUTIONS? #shorts
Views : 7,310
Genre: Howto & Style
License: Standard YouTube License
Uploaded At Jul 5, 2023 ^^
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RYD date created : 2024-01-14T18:29:56.117313Z
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22 Comments
Top Comments of this video!! :3
Lambert W function:
W(ne^n)=n
xlnx=2048ln2
(lnx)e^lnx=2048ln2
W(lnxe^lnx)=W(2048ln2)
lnx=W(2048ln2)
x=e^W(2048ln2)
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Wow
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That does not prof that x=256 is the only solution, so from that we don't know that we got all the solutions. The is the only integer solution (there is a family of complex solutions) but we did not show it.
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x^x = 2 ^ (2048) =( 2 ^ n) ^ ( 2 ^ 11 / n)
Hereby
2 ^ n = 2 ^ (11) / n.
2 ^ ( n - 11) = 1/ n
has a trivial solution at n = 8
Hereby x = 2 ^ 8 = 256
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💗
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I can also calculate 256 by myself😊 but I'm surprised that this is a short vide
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x^x= 2^2048
x^x= 2^8(256)
x^x = 256^256
x=16^2//
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x^x = 2^2048 = 256^256
x = 256
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Say you're gonna solve with Law of Indices instead of Power rule of Exponents. Sometimes ya gotta throw a curve ball. 🙂
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I found a general solution of xln(x) = 16²ln(16²)
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x^x=2^(2^11)
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X is 256
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x=256
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No...
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2¹¹
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X = 256
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@bigm383
1 year ago
I honestly doubted that the Professor could do a short video, because he is such a perfectionist, but here it is!
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