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42,656 Views • Dec 19, 2022 • Click to toggle off description
Views : 42,656
Genre: Education
Uploaded At Dec 19, 2022 ^^
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RYD date created : 2023-02-04T03:15:45.06148Z
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YouTube Comments - 108 Comments
Top Comments of this video!! :3
That’s not solving. That’s guessing. Lol. Let’s see you use algebra to derive that x = -2.
224 |
Here’s a tough problem:
So step one let’s just plug in the answer-
48 |
x^x = 1/4
take ln of both sides
ln(x^x) = ln(1/4)
xln(x) = ln(1/4)
we turn x into e^ln(x) as its the same
e^ln(x)ln(x) = ln(1/4)
We see a lambert W function pattern here
W(e^ln(x)ln(x)) = W(ln(1/4)
ln(x) = W(ln(1/4))
x = e^(W(ln(1/4)
2 |
Oh, so the method is to already know the answer before you start solving the problem. Cool.
36 |
Yes but how did you find that X is -2????
(His answer: well, I looked at the solutions page, and plugged in the answer...)
10 |
X^x = 1/4
So X^x = 1/2^2 or X^x = 1/-2^2
Solving First further we get X^x = 2^-2 which is rejected
Now by second we get X^x = -2^-2
So X = -2
1 |
That does not show how to derive the answer but merely a check on the actual right number. I did that, but I don't consider it solving the equation by any more than making an informed guess.
Also, that answer doesn't prove that it's unique either (although if you look at how it diverges for smaller and larger values of x it becomes fairly obvious that there aren't any more real solutions).
1 |
thats just guessing...
17 |
X=-2
-2^-2=1/4
1 |
Now I’m pretty sure this function only exists in the positive x-domain. My memory might be wrong but this function isn’t continuous at the point x=0, meaning you can only evaluate it at x>0. (Lim as x->0 from left side trends to -1 and lim as x->0 from right side trends to 1 (supposedly).)
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worst teacher in a long time. cheated by having the answer ahead of time, and explained nothing.
2 |
Who gave you the answer?
3 |
well x can be 1/2 also..
1 |
xln(x) = ln(1/4) = -ln(4). So:
ln(x) e^ ln(x) = -ln(4). So,
ln(x) = W(-ln(4))
x = exp(W(-ln(4))
Using different branches of W may get u more solutions, but -2 is certainly the result of one of the branches
5 |
That is not solving at all, you start writing the answer straight away.
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I can’t tell if this is ironic.
1 |
Derivation please.
How come number -2
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thats just a lucky guess, not "solving" it algebraically. to solve it you would require the lambert w function
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Ah yes good old guessing
1 |
@DrLiangMath
1 year ago
For more nice math videos, please watch youtube.com/@DrLiangMath
2 |