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If 5^n > 10,000, and n is an integer, the smallest possible value of n

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Bunuel
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If 5^n > 10,000, and n is an integer, the smallest possible value of n [#permalink] New post   24 Dec 2018, 23:38
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If 5^n > 10,000, and n is an integer, the smallest possible value of n is


A. 4
B. 5
C. 6
D. 7
E. 8
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C
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If 5^n > 10,000, and n is an integer, the smallest possible value of n [#permalink] New post   Updated on: 06 Jan 2019, 06:56
Bunuel wrote:
If 5^n > 10,000, and n is an integer, the smallest possible value of n is


A. 4
B. 5
C. 6
D. 7
E. 8

5^n > 10,000,

10,000 = 5^4*2^4

so n has to be >5

IMO C 6

Originally posted by Archit3110 on 25 Dec 2018, 08:08.
Last edited by Archit3110 on 06 Jan 2019, 06:56, edited 1 time in total.
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Re: If 5^n > 10,000, and n is an integer, the smallest possible value of n [#permalink] New post   06 Jan 2019, 06:53
If 5^n > 10,000, and n is an integer, the smallest possible value of n is

10,000= (2*5)^4

5^4= 625
5^5= 3125
5^6= 15515

answer= 6
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If 5^n > 10,000, and n is an integer, the smallest possible value of n [#permalink] New post   06 Jan 2019, 07:22
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If \(5^n > 10,000\), and n is an integer, the smallest possible value of n is

\(10,000 = 5^4*2^4\)
\(2^4 = 16 >5 But 16 < 25 i.e., 5^2\)
implies 5^4 * 5^2 i.e., \(5* 5^4 < 16 * 5^4 < 25* 5^4\)

minimum value of n is 6
Option C is correct
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Re: If 5^n > 10,000, and n is an integer, the smallest possible value of n [#permalink] New post   13 Feb 2023, 07:27
If 5^n > 10,000, and n is an integer, the smallest possible value of n is

Here 5^n is greater than 2^4 * 5^4

A. 4 when we take n = 4 then it becomes 5^4 which is smaller than 2^4 * 5^4. So incorrect
B. 5 For n = 5 we can write it as 5 * 5^4. here 5 < 2^4. So it is incorrect too.
C. 6 For n = 6 we can write it as 5^2 * 5^4, here 5^2 > 2^4 so condition is satisfied
D. 7 For n = 7 we can write it as 5^3 * 5^4, here 5^3 > 2^4 so it is also true
E. 8 For n = 8 we can write it as 5^4 * 5^4, here 5^4 > 2^4 so it is true too.

but we have been asked minimum value of n. So option C, n = 6, is correct.
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Re: If 5^n > 10,000, and n is an integer, the smallest possible value of n [#permalink] New post   23 Apr 2023, 01:24
5^n > 10000
5^n > 5^4 x 4^2
5^(n-4) > 4^2
5^(n-4) > 16

For the inequality to hold true, the least possible value n can take on is 6.

5^(6-4) > 16
5^(2) > 16
25 > 16
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Re: If 5^n > 10,000, and n is an integer, the smallest possible value of n [#permalink]
23 Apr 2023, 01:24
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