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What is the smallest integer n for which 25^n > 5^12 ?
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29 May 2020, 11:11
29 May 2020, 11:11
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Re: What is the smallest integer n for which 25^n > 5^12 ?
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29 May 2020, 11:12
29 May 2020, 11:12
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Re: What is the smallest integer n for which 25^n > 5^12 ?
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29 May 2020, 11:15
29 May 2020, 11:15
1
Carcass wrote:
We have: 25^n > 5^12
To rewrite this inequality with the SAME base, we'll replace 25 with 5².
When we do so, we get: (5²)^n > 5^12
Apply the Power of a Power law to get: 5^(2n) > 5^12
This means that it must be the case that 2n > 12
Divide both sides of the inequality by 2 to get: n > 6
What is the smallest integer n for which 25^n > 5^12 ?
We now know that n > 6
So, 7 is the smallest possible INTEGER value that satisfies this inequality.
Answer: 7
Cheers,
Brent
