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What is the greatest integer, x , such that
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13 Jul 2020, 08:04
13 Jul 2020, 08:04
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What is the greatest integer, x , such that \(\frac{125^x}{25^6}<1\) ?
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Show: :: OA
3
Re: What is the greatest integer, x , such that
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13 Jul 2020, 16:32
13 Jul 2020, 16:32
multiplied 25^6 both sides. Factored 125 and 25 to have same base. Resulted with X < 4. Therefore the largest integer that satisfies that condition is 3.
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Re: What is the greatest integer, x , such that
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03 Aug 2020, 05:51
03 Aug 2020, 05:51
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Carcass wrote:
What is the greatest integer, x , such that \(\frac{125^x}{25^6}<1\) ?
Kudos for the right answer and explanation
Kudos for the right answer and explanation
Show: :: OA
3
Given: \(\frac{125^x}{25^6}<1\)
Multiply both sides of the inequality by \(25^6\) to get: \(125^x<25^6\)
Rewrite \(125\) and \(25\) as powers of \(5\) to get: \((5^3)^x<(5^2)^6\)
Apply the Power of a Power law to get: \(5^{3x}<(5^{12}\)
From this we can conclude: \(3x < 12\)
Divide both sides by \(3\) to get: \(x < 4\)
So the greatest possible INTEGER value of \(x\) is \(3\)
Answer: 3
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