Friday, May 16, 2008

Googol to the Googol-th Power

Target DiagramAt this point everyone should be familiar with the number "googol" which is 10^100 (10 to the 100th power). Written down it is a one followed by 100 zeroes.

The question this week is:
Q: How many zeroes are there in googol^googol
(googol to the "googol-th" power)?

2 comments:

  1. Eric is right. To figure the number of zeroes, just take the common log:

    log(googol^googol)

    Use this rule: log(a^b) = b log(a)
    = googol * log(googol)
    = googol * log(10^100)

    Use the rule again:
    = googol * 100 * log(10)

    Finally log(10) is simply 1:
    = 100 googol * 1
    = 100 googol

    Answer:
    One hundred googol zeroes

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