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If n is an integer and 5^n > 4,000,000, what is the least
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19 Feb 2012, 19:02
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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
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Re: If n is an integer and 5^n > 4,000,000, what is the least
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21 Feb 2012, 14:05
Answer should be D. Here is how I solved it. Original Statement: \(5^n>4,000,000\) so \(5^n>4*10^6\) so \(5^n>4*2^6*5^6\) dividing by 5^6 on both sides leads to: so \(5^{n6}>2^8\) so \(5^{n6}>256\) Now we know that \(5^3=125\) so it has to be that the number is \(5^4\), the least number that is greater than \(256\) so \(n6=4\) so \(n=10\) Hence D.
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Re: If n is an integer and...
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19 Feb 2012, 21:42
vix 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 Make prime factorization of \(4,000,000=2^2*1,000,000=2^2*(10^6)=2^8*5^6=256*5^6\). So, we have: \(5^n>256*5^6\) > \(5^4=625>256\) (5^3=125<256), so \(5^n\) must be at least equal to \(5^4*5^6=5^{10}\) to be more than \(256*5^6\). Hence, the least possible value of n is 10. Answer: D. Hope it's clear.
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Re: If n is an integer and...
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09 Aug 2012, 13:17
I may be wrong here but with the question written as 5^n <4000000, and wanting the least possible value for n, it would just be the lowest answer choice (7) since it will easily be under 4000000



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Re: If n is an integer and...
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09 Aug 2012, 13:40
sdrobbi wrote: I may be wrong here but with the question written as 5^n <4000000, and wanting the least possible value for n, it would just be the lowest answer choice (7) since it will easily be under 4000000 Really sorry, I made a mistake on the sign. Corrected, thx..



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Re: If n is an integer and...
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09 Aug 2012, 14:59



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If n is an integer and 5^n > 4,000,000, what is the least possib
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29 Sep 2012, 23:18
Hi everyone, This is an old thread, however I do have a question. Are we supposed to know value such as 2^9 off the top of our head? Thanks for your help



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Re: If n is an integer and 5^n > 4,000,000, what is the least po
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01 Oct 2012, 06:42



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Re: If n is an integer and 5^n > 4,000,000, what is the least
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20 Nov 2013, 12:42
here is my approach  5^n > 4000000. => (10/2)^n > 4000000 .. now 10^10 will have 1 followed by 10 zeros. Dividing by 2^10 = 1024, the expression will become 10^7/1.024. its simple to see 10^9/512 means 1000000/5.12 < 4000000.
If you know the values of power of 2 (which I think is really helpful), you might do calculation this way in mind implicitly.



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If n is an integer and 5^n > 4,000,000, what is the least
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03 Mar 2016, 22:03
My approach
5^2 = 25 5^3 = 125 5^4 = 625 5^5 = 3.X thousand 5^6 = 1618K 5^7 = ~80k 5^8 = ~450K 5^9 = ~2 mil 5^10 = less than 40 mil, therefore the highest answer is 11. E



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Re: If n is an integer and 5^n > 4,000,000, what is the least
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09 Mar 2016, 23:41



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Re: If n is an integer and 5^n > 4,000,000, what is the least
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02 Jul 2017, 10:17
5^n > 4000000. => (10/2)^n > 4000000 .. now 10^10 will have 1 followed by 10 zeros. Dividing by 2^10 = 1024, the expression will become 10^7/1.024. its simple to see 10^9/512 means 1000000/5.12 < 4000000.
SO , ans is 10. D



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Re: If n is an integer and 5^n > 4,000,000, what is the least
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12 Jul 2017, 09:46
vix 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 I thing we can convert the above question as \(5^n > 4,000,000 ..... sqrt(5^n) > 2,000 .....5^n/2 > 2,000\) now it is much easier to find the value of n/2 so it \(5^n/2\) greater than 2000. \(5^n/2 > 2,000 ... 5^5 > 2000\) so n/2 = 5 and n = 10.



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Re: If n is an integer and 5^n > 4,000,000, what is the least
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16 Jul 2017, 17:24
vix 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 Let’s break 4,000,000 into primes: 4,000,000 = 4 x 10^6 = 4 x 2^6 x 5^6 = 256 x 5^6. So, we have: 5^n > 256 x 5^6 We see that n will definitely have to be greater than 6. We have to figure out what power of 5 is going to get us to a number greater than 256. We see that 5^3 = 125 isn’t big enough, but 5^4 = 625 fulfills our requirement of being greater than 256. Thus, n will be (6 + 4) = 10, because it is true that 5^10 > 256 x 5^6. Answer: D
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Re: If n is an integer and 5^n > 4,000,000, what is the least
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Re: If n is an integer and 5^n > 4,000,000, what is the least
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