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Year by Year (Posted on 2004-11-23) Difficulty: 4 of 5
Consider N=2004^2004.

1) What are the first 3 digits of N?

2) What are the last 3 digits of N?

See The Solution Submitted by SilverKnight    
Rating: 2.3333 (6 votes)

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Solution Solution To Part I | Comment 6 of 8 |

N = 2004^2004

Taking log on both sides, we obtain:

log N = 2004*log 2004
= 2004*3.3018977171952
= 6617.003025259 (correct to 9 decimal places)

Accordingly,
N = (10^.003025259)*(10^6617)
= (1.0069902)*(10^6617)
= (100.69902)*(10^6615)

Consequently, the first three digits of N are 100

Edited on October 18, 2007, 9:28 am
  Posted by K Sengupta on 2007-10-18 06:27:12

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