Awesome!

Nice!

Very good

@KnowledgeTricks470

Ай бұрын

Thank you 😊

Are there more non-integer solutions? If you left x=1 the left side is larger. If you let x=2 the right side is larger. I think this implies there is another solution between x=1 and x=2.

@user-ww6gw8ns5j

Ай бұрын

Согласен, есть

But what is done on one side of equality does not have to be done on the other ?

How do you know that this equation has no other solution?

@quixata

Ай бұрын

Use the product-log function to get all the solutions

@KnowledgeTricks470

Ай бұрын

We can use Lambert function to get the solution

@quixata

Ай бұрын

@@KnowledgeTricks470 yes... that is the product-log....inverse of x(e^x)

@KnowledgeTricks470

Ай бұрын

@@quixata yes , you're right 👍🏻

@quixata

27 күн бұрын

@@KnowledgeTricks470 no.... usage of product-log (Lambert W) function will give all the solutions. But the equation in question, has only one real root and that is x=256. Modified equation is 256^(1/256) = x^(1/x). The function on the right hand has a critical point at x=e and when x