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10 ^(2n)  < 25000000  take the log of  both sides

log 10^(2n)  < log ( 25000000)

(2n)  < log (25000000)  / log 10                    (log 10 =  1)

2n < log (25000000)

n<  log (25000000) / 2   ≈   3.698   →    n <  ≈ 3.698

Similarly we would have

log (25000000) < 10^( 2n + 1)

[ log (25000000) - 1] / 2  < n  →     n >   ≈  3.19

The integer value of n =  3