Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

How is the best way to compare big numbers? They are result of two functions with different asymptotic growth. For example:

Googleplex which is $10^{{10}^{100}}$ to $1000!$

share|cite|improve this question
You might look at… – Ross Millikan Jul 22 '12 at 1:07
Take logarithms. Use Stirling's formula. – Qiaochu Yuan Jul 22 '12 at 1:32
Apropos to Ross's comment, see this article as well. – J. M. Jul 22 '12 at 3:55
up vote 6 down vote accepted

$10^{googol}$ compared to $1000!$



since a googol is drastically larger than $3000$, the first number is much, much greater.

In general logarithms (equivalently, converting to a base and comparing exponents) are a great way for comparing large numbers. For example: whether $2^{523} <^? 3^{228}$ may not be obvious, but even knowing very rounded values for $\log(2)$ and $\log(3)$ will let you compare $523\log(2)$ and $228\log(3)$ quite easily, which is an equivalent problem.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.