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