Prove the inequality for the indicated integer values of n

I deleted my earlier entry because my reasoning was incorrect.  Here is (what I hope is) a correct proof:

lhs = (9/7)^n
rhs = n

When n = 9  lhs = 9.6...   rhs = 9   so lhs > rhs

When n increments by 1 the lhs increments by (9/7)^n(9/7 - 1) = (2/7)*(9/7)^n
The smallest value of this (for n >= 9) is 2.7...,  given when n = 9, and gets larger as n increases.

When n increments by 1 the rhs increments by n + 1 - n or just 1 for all n.

Hence the lhs starts larger than the rhs (where start is n = 9) and increases more rapidly than the rhs as n increases.

i.e. (9/7)^n > n for all n>=9

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This is  looks pretty obvious when a graph is plotted: