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Which is bigger 2^999 or 999^2

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Which is bigger 2^999 or 999^2

Note: solve without calculating it...

posted Mar 21 by anonymous

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1 Answer

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Log function gives us an idea of how many zeros a number has if Log base 10 is used.
Log(2^999) = 999×Log 2 = 999×0.3010 ≈ 1000×0.3010 ≈ 301
Log(999^2) = 2×Log 999 ≈ 2×Log 1000 ≈ 2×3 ≈ 6
Therefore as Log(2^999) > Log(999^2) => 2^999 > 999^2

answer Mar 21 by Tejas Naik



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