# how to force simplification of power inequalities

These two simple expressions fail to simplify (Mma 11.1):

FullSimplify[Power[x, n] < Power[y, n], Assumptions -> 0 < x < y && n >= 1]
FullSimplify[1 < Power[y/x, n], Assumptions -> 0 < x < y && n >= 1]


Logarithmic transformation helps; this works:

Simplify[Log /@ (Power[x, n] < Power[y, n]), Assumptions -> 0 < x < y && n >= 1]


Can I force simplification of the first two?

• FullSimplify[1 < Power[a, n], Assumptions -> a > 1 && n >= 1] doesn't simplify either. No need for 3 variables. – user202729 Jul 1 '18 at 11:24
• Or even FullSimplify[1 < Power[a, a], Assumptions -> a > 1]. – user202729 Jul 1 '18 at 11:24