What number tetrated by itself equals a googol?

Question

http://en.wikipedia.org/wiki/Tetration

Tetrating stuff makes it really big really fast. I'm trying to figure out what number would equal a googol. Any help?

Or a googolplex ?

Answer 1

We use essentially guess and check.

Consider $X = 3$

Then:

$$Tetration(3,3) = 3^{(3^3)} = 3^{(27)}$$

Too small, lets try bigger

$$Tetration(4,4) = 4^{(4^{4^4})} = 4^{4^{256}} \text{~ ~} 4^{10^{155}} $$

That's getting better. Interpolating any further is tricky business and may require some specialized tools.

The users here: http://math.eretrandre.org/tetrationforum/index.php

Would probably be well equipped to answer your question