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If 3^x – 3^(x – 1) =2(3^13), what is x?

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If 3^x – 3^(x – 1) =2(3^13), what is x? [#permalink]

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New post 25 Apr 2017, 02:45
1
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A
B
C
D
E

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  15% (low)

Question Stats:

87% (01:05) correct 13% (01:43) wrong based on 87 sessions

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Re: If 3^x – 3^(x – 1) =2(3^13), what is x? [#permalink]

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New post 25 Apr 2017, 03:14
3^x - 3^(x-1) = 3^(x-1) [3-1] = 3^(x-1) * 2

So, according to question, 3^(x-1) = 3^13 ---> x-1=13 ---> x=14

Hence, answer will be B.
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If 3^x – 3^(x – 1) =2(3^13), what is x? [#permalink]

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New post 01 May 2017, 06:28
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\(3^{x}\) - \(3^ {(x-1)}\) = 2 (\(3^{13}\)). What is x?

\(3^{x}\) - (\(3^{x}\))(\(3^{-1}\)) = 2 (\(3^{13}\))
\(3^{x}\) (1-\(\frac{1}{3}\)) = 2 (\(3^{13}\))
\(3^{x}\)( \(\frac{2}{3}\)) = 2 (\(3^{13}\))
2 (\(3^{-1}\))(\(3^x\)) = 2 (\(3^{13}\))
2 (\(3^{x-1}\)) = 2 (\(3^{13}\))
x-1 = 13
x = 14 ... Answer B

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Re: If 3^x – 3^(x – 1) =2(3^13), what is x? [#permalink]

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New post 01 May 2017, 09:21
Bunuel wrote:
If \(3^x – 3^{(x – 1)} =2(3^{13})\), what is x?

(A) 13
(B) 14
(C) 15
(D) 16
(E) 17


\(3^x – 3^{(x – 1)} =2(3^{13})\)

Or, \(3^x – \frac{3^x}{3} =2(3^{13})\)

Or, \(3*3^x - 3^x = 2*3^{14}\)

Or, \(3^x ( 3 - 1 ) = 2*3^{14}\)

Or, \(2*3^x = 2*3^{14}\)

So, \(x = 14\)

Hence, the answer must be (B) 14
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Re: If 3^x – 3^(x – 1) =2(3^13), what is x? [#permalink]

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New post 01 May 2017, 10:04
It easier if we substitute answers for this question

x = 13, will not make sense, because x^13 - x^12 cannot be 2(3^13)

Use x=14
3^14 - 3^(14-1)
=3*3^13 - 3^13
=3^13(3-1)
=2*(3^13)

Hence, we have our answer, Option B.
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Re: If 3^x – 3^(x – 1) =2(3^13), what is x?   [#permalink] 01 May 2017, 10:04
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