Which of the following is the largest number? 2^4000, 3^3000, 4^2500, 5^2000 **no calculator or logarithm tables.

(In reply to Answer by K Sengupta)

At the outset, we observe that:

2^4000 = (2^4)^1000 = 16^1000

3^3000 = (3^3)^1000 = 27^(1000)

4^2500 = 2^5000 = (2^5)^1000 = 32^1000

5^2000 = (5^2)^1000 = 25^1000

Since 16< 25< 27< 32, it follows that:

 16^1000 < 25^1000 < 27^1000 < 32^1000

Consequently, 4^2500 is the largest number.

Edited on March 28, 2008, 6:12 am

Posted by K Sengupta on 2008-03-28 06:11:25