3<100^1/n<5

3ⁿ<100<5ⁿ

So, 3ⁿ<100                                       and                                100<5ⁿ

i.e.n=1,2,3,4                                    and                                 n=3,4,5,6,7.......................................

Form both the values of n we got above we have 3&4 common value of n in both cases.

Hence n=[3,4]

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3<100^1/n<5

so 3^n,100,5^n

is true for n=3 and 4       P S Dave M.Sc BEd (maths)