- Thread starter
- #1

- Thread starter soroban
- Start date

- Thread starter
- #1

- Admin
- #2

- Aug 18, 2013

- 76

- Mar 22, 2013

- 573

A Perelman-like solution suffices :

$-\lg \, \log_{\sqrt{4}} \, \underbrace{\sqrt{\sqrt{...\sqrt{4}}}}_{\text{65 times}}$

Or even,

$4^\left ({\log \sqrt{\sqrt{\sqrt{e^{4!}}}}} \right )$

But as $\log$ is not desired, a twist around the base of logarithm of the latter should do :

$\sqrt{\sqrt{\sqrt{4^{4!}}}}$

Last edited:

- Thread starter
- #5

- Mar 22, 2013

- 573

Okay, thanks! The other form didn't click to me, really nice!

Now, in my post, the first form using logarithm is referred to as "Perelman-like" as another related, but twisted problem was given in Yakov Perelman's Mathematics Is Fun. He refers a challenger in a congress of physicist in Odessa. I couldn't find further reference, so just named this after him. (a year ago when I found out this kind of approach is in general very doable for these problems)