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Re: x > 1 [#permalink]
Carcass wrote:
Is that explanation complete ?? :roll:


Yes, I was just seeing if I my coding was correct.
It's complete now.
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Re: x > 1 [#permalink]
1
Carcass wrote:
\(x > 1\)

Quantity A
Quantity B
\(5^x +1\)
\(6^x\)



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Kudos for the right answer and explanation



Given that \(x > 1\), we need to compare:

Quantity A: \(5^x + 1\)
Quantity B: \(6^x\)


\(5^x + 1\) VS \(6^x\)

Divide both sides by \(5^x\):

\((5^x + 1)/5^x\) VS \(6^x/5^x\)

Or \((1 + 1/5^x)\) VS \((6/5)^x\)

Or \((1 + 1/5^x)\) VS \((1 + 1/5)^x\)

The term \((1 + 1/5)^x\) can be expanded using binomial expansion to get: \(1^x + ... \) (many terms in-between) \( ... + (1/5)^x\)

Thus, Quantity B is greater than Quantity A

Answer B
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Re: x > 1 [#permalink]
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Re: x > 1 [#permalink]
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