INDIAN Entrance Examination | How to Compare two numbers without Calculator | Which is bigger?

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(5/4)^4311 < (5/4)^5000 = [(5/4)^5]^1000 = [(5/4)^4*(5/4)]^1000 = [(625/256)*(5/4)]^1000 < [3*(5/4)]^1000 =
= (15/4)^1000 < (16/4)^1000 = 4^1000
=> 5^4311 < 4^4311*4^1000 = 4^5311