# Let #x in ZZ^+# and #y=x^x# s.t. #x=floor(ln(y))#. For what value(s) of #x# will this hold?

##
This was a problem I came up with for my birthday a couple of weeks ago...

This was a problem I came up with for my birthday a couple of weeks ago...

##### 2 Answers

Void.

#### Explanation:

I posted this question a year ago for fun. Since I have received no answers I will post my solution.

Since

Also, we know by properties of the floor function that

Combining both statements we have the inequality

Thus

Claim:

Since

Thus is suffices to show that

Since

Thus,

I came up with this problem because last year I turned

So today I am