If n is an integer and 5^n > 4,000,000, what is the least possible value of n? (A) 7 (B) 8 (C) 9 (D) 10 (E) 11

5^n > 4,000,000 5^n > 4*(10^6) 5^n > 4*(5^6)*(2^6) 5^n > 256 * (5^6) 5^3<256<5^4 Min value of n = 10 IMO D

sanju09 wrote:If n is an integer and 5^n > 4,000,000, what is the least possible value of n? (A) 7 (B) 8 (C) 9 (D) 10 (E) 11 5^n > 4,000,000 5^n > 2² * 10^6 5^n > 2² * 2^6 * 5^6 5^n > 2^8 * 5^6 5^(n - 6) > 256 Now 5^4 = 625 > 256 So, n - 6 = 4 n = 10 The correct answer is D.

Anurag@Gurome wrote:sanju09 wrote:If n is an integer and 5^n > 4,000,000, what is the least possible value of n? (A) 7 (B) 8 (C) 9 (D) 10 (E) 11 5^n > 4,000,000 5^n > 2² * 10^6 5^n > 2² * 2^6 * 5^6 5^n > 2^8 * 5^6 5^(n - 6) > 256 Now 5^4 = 625 > 256 So, n - 6 = 4 n = 10 The correct answer is D. Hi, I got lost at: This line: 5^n > 2^8 * 5^6 Could you explain its following: 5^(n - 6) > 256 Now 5^4 = 625 > 256 Thanks

Though directed to Anurag, I will try to explain it my way 5^n > 4,000,000 5^n > 2² * 10^6 5^n > 2² * 2^6 * 5^6 5^n > 2^8 * 5^6 5^(n - 6) > 256 125 < 256 < 625. 5^3 < 256 < 5^4 5^3 < 256 < 5^(n - 6) Since we need the least integer value of n in 5^(n-6), the value of 5^(n-6) should be 5^4 which is the immediate next power of 5. Now 5^4 = 5^(n-6) So, n - 6 = 4 n = 10 Hope that helps !

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