I Solved A Nice Exponential Equation With The Natural Log

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[@kianmath71]

X = W(sqrt(e)/2) = 1/2

[@arolimarcellinus8541]

I got that result too. But how you know that it will be 1/2?? It means W(sqrt(e))=1???

[@hazwi]

@@arolimarcellinus8541 its W[sqrt(e)/2] so basically W[0.5*e^(0.5)) which is 0.5 which is 1/2

[@adrianjanik6569]

1:22 Why do we have -lne on the right side? Instead of -ln2?

[@adrianjanik6569]

OK. Corrected at 2:10. I have to be more patent 😢

[@vashon100]

@@adrianjanik6569 patient vs patent

[@jamesharmon4994]

​@adrianjanik6569 me too 😅

[@adrianjanik6569]

😂

[@ManjulaMathew-wb3zn]

Method 3 on me.
One of the steps in method 2 you had
e^x . e^lnx = (1/2) e^(1/2). However 1/2 = e^(ln(1/2)).
Substituting and re arranging
e^x . e^lnx = e^(1/2) . e^(ln(1/2)).
Again from one to one correspondence you get x=1/2. No lambert w is needed.
For all real x the domain is x>0 so f’(x) = 1+ 1/x is always positive and f(x) is an increasing function which can intersect a horizontal line only once thus only one real solution which is 1/2.
f”(x) = -1/x^2 always negative. So no inflexion points of f(x) and it curves down as x increases and will become flat as x approaches infinity.
I love how you explain graphs. Also I love the fact you don’t waste time on explaining simple rules when handling a complex problem. If the audience can handle the problem they sure will know basics. I love that strategy.

[@trojanleo123]

x = 1/2. Rearranged and used Lambert W function.

[@RobG1729]

I watch and appreciate all of your videos.
If you did live streams, we viewers would be pointing out mistakes before you catch them.

[@MrVanderreijden]

I think they area bir reverse engineered sometimes.

[@barakathaider6333]

👍

[@johns.8246]

Here's a tough one for you. For which natural numbers n does n+1 divide n!+2 and why?

[@GreenMeansGOF]

x=W_n(sqrt(e)/2) over all branches.

[@user-lq2mn6wy7f]

Cool

[@mcwulf25]

The lhs is xe^x. Whatever could that mean?

[@vashon100]

Are you familiar with exponents?

[@mcwulf25]

@@vashon100 I was being ironic.

[@vashon100]

@@mcwulf25 A situation can be ironic, a person can be sarcastic.

[@jpbobinus1377]

🎉❤😂

[@rob876]

xe^x = (1/2)e^(1/2)
x = 1/2

[@ftorum19]

x=W(sqrt(e)/2)=1/2

[@msmbpc24]

X=1/2

[@giuseppemalaguti435]

x=W...