Question

What is the greatest number that can be written with the digits two, five, eight

Answer 1

Using each of those numbers as digits of a number then it is 852

However, if we raise each number to a power then 2^(5^8) where

5^8 = 390,625  So, 2^390,625 can be estimated by

multiplying the log of 2 (0.30102999566) by 390,625 which equals

117,589.842054688   So, 117,589 is our exponent and then we need to look up the anti-log of .842054688 which equals  6.9511184318 and our number is  6.9511184318 x 10^117,589

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Answer 2

$2^{5^{8}}$

that is a number with more than 100,000 digits