If n is an integer, and 5^n > 4,000,000 then what is the least possible value of n ?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Prajakt wrote:If n is an integer, and 5^n > 4,000,000 then what is the least possible value of n ?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Prime factorization of 4,000,000 = 2² * 1,000,000 = 2² * 10^6 = 2^8 * 5^6 = 256 * 5^6
So, 5^n > 256 * 5^6
5^4 = 625, which is greater than 256 and 5^3 = 125 < 256
So, 5^n should at least be equal to 5^4 * 5^6 = 5^10 for 5^n > 256 * 5^6 to hold true.
Therefore, the least possible value of n is 10.
The correct answer is D.
