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A great algebra question today (for advanced students).What do you think about this algebra problem? If you're reading this ❤️. Have a great day!

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[brnmcc]

You can also simplify the answer a little bit to take the natural log of the square root of 3, since a^(log(x)/2) is the same as a^(log(sqrt(x))). So X would be equal to e^(W(log(sqrt(3)))×2) in plain text.

[berntfritiofulveborn]

Really nice presentation but could you link to some good Lambert function calculators 👍🙂

[RyanLewis-Johnson-wqxs]

X^Sqrt[X]=3 X=e^(2W(Ln(3)/2))=e^(2W(Log[e^2, 3]))

[rexford]

Or you can raise both sides to the 1/√x power and then multiply both sides by -1/2, then apply W function.

[PerezKwadwoAwuah]

I don’t know if my method is also right but I got a different answer though. Let’s see

Let y = sqrt(x)

yln(x) = ln(3)

(1/2)yln(x) = (1/2)ln(3)

yln(y) = ln[sqrt(3)]

e^(yln(y)) = e^(ln[sqrt(3)])

ye^y = sqrt(3)

W(ye^y) = W(sqrt(3))

y = W(sqrt(3))

But y = sqrt(x)

sqrt(x) = W(sqrt(3))

(sqrt(x))^2 = [ W(sqrt(3)) ]^2

x = [ W(sqrt(3)) ]^2

Is it?😶

[RyanLewis-Johnson-wqxs]

Ln(3)/2=Log[e^2, 3] Input I just proved that it could be simplified.
Ln(3)/2 =Log(e^2, 3)
Results
True
True

[ManojkantSamal]

X is in between 2 &3
Respected Sir, Good evening... Pls get me the whole of Lambert aw function....

[ManojkantSamal]

*=read as square root
^= read as to the power
According to the question
X^(*x)=3Take the square
(X^(*x)}^2=3^2
X^x=3^2
(X^x)^(1/x)=(3^2)^(1/x)
X=3^(2/x)
Take the log
X=9^(1/x)

[liejdbdj-g]

미국 어학연수 생활비 대출 좀 해줘 대출좀 그런데 난 대출 안좋아하고 소출 좋아해 소출

[prollysine]

let u=Vx, Vx*lnx=ln3, u*ln(u^2)=ln3, 2*u*lnu=ln3, u*lnu=(ln3)/2, lnu=W((ln3)/2), u=e(W((ln3)/2), Vx=e^(0.376838695), Vx=~ 1.45767,
Vx=~ 1.45767^2, x=`~ 2.1248, test, x^Vx= 2.1248^1.45767 --> 3, OK,