May be easy.......

{\color{red} 17^{14}>31^{11}-\mathit{Prove...}}

3 Answers

use 17=16+1

and 31=32-1

I think that should seal the deal :)

Solution is hidden below :)

LHS > 16^14=2⁵⁶

RHS < 32^11 = 2⁵⁵

also 2⁵⁶>2⁵⁵

Hence done :)

Excellent good job still I am posting the solutions................for others17^{14}>16^{14}=(2^{4})^{14}=2^{56}>2^{55}=(2^{5})^{11}=32^{11}>31^{11}

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