Ratio of 2012 power to 2013 power

Let: f (x)=[ lnx ]/(x) then: f'(x)=(1-lnx)/(x2) then: the function f (x) decreases when x > e, then: f (2012)> f (2013)[ ln2012]/(2012)>[ ln2013]/(2013)2013ln2012>2012ln2013ln [2012^2013]> ln [2013^2012]2012^2013>2013^2012...

A power of A=2×2014 power of 3,2013 power of B=2×2012 power of 3, size of A and B, A power of A=2×2014 power of 3,2013 power of B=2×2012 power of 3, compare the sizes of A and B,

A=2 power of 2011×3 power of 2012×3 square
B=2 2011×3 2012×2 square
Because 9>4
So A > B
(Take the formula apart to see it.)

A=2 power of 2011×3 power of 2012×3 square
B=2 2011 power ×3 2012 power ×2 square
Because 9>4
So A > B
(Take the formula apart to see it.)

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