Question

If \((\sqrt{x})^{\sqrt{x}}=y\) then \(x\) is equal to :-

Answer 1

@experimentX @satellite73 @ParthKohli plz help

Answer 2

help...

Answer 3

\[\LARGE{(x^{1/x})^{x^{1/x}}=y}\]by taking log on both sides\[\LARGE{\log(x^{1/x})^{x^{1/x}}=y}\]\[\LARGE{logx^x=y}\]nt sure

Answer 4

just let sqrt(x) = a for simplicity's sake.

Answer 5

k!

Answer 6

a^a=y

Answer 7

wht's the next step ?

Answer 8

i don't have one ... need to work out on this. since this is one to one function, there must be inverse. I wonder if this is easily possible.

Answer 9

but i do not know anything :P

Answer 10

@phi

Answer 11

I think you have to use the product log function.
http://en.wikipedia.org/wiki/Lambert_W_function

Answer 12

really ?

Answer 13

I'm nt sure about this since it is a topic of calculus :P

Answer 14

I dont see this question as solvable unless you have knowledge about interpolation.

Answer 15

i don't know interpolation, sorry :P

Answer 16

You can not solve for x from here. Please recheck the question.

Answer 17

I mean one can, but that is out of scope.

Answer 18

What is the question?