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BIG , BIGGER , BIGGEST (Posted on 2004-08-12) Difficulty: 2 of 5
Which of the following is the largest number? 2^4000, 3^3000, 4^2500, 5^2000 **no calculator or logarithm tables.

See The Solution Submitted by Ady TZIDON    
Rating: 3.0000 (4 votes)

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My Solution - comments? | Comment 1 of 8

Start by comparing 2^4000 and 4^2500 clearly the latter is 2^5000 and so larger, we can thus ignore 2^4000

Then noting that 3^3 is 27 and 5^2 is 25 we have

27^1000 and 25^1000, thus 3^3000 is larger than 5^2000

thus we only need to compare 4^2500 and 3^3000

looking at powers 4^2.5 is 4^2 * 4^0.5 or 16*2 = 32

3^3 is 27

so we have 3^3000 = 27^1000

and 4^2500 = 32^1000

So I reckon that 4^2500 is the largest, without the use of calculators or log tables.

David  

 


  Posted by David Bate on 2004-08-12 07:21:01
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