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

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Joined: 02 Sep 2009
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If 3^x – 3^(x – 1) =2(3^13), what is x?  [#permalink]

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25 Apr 2017, 02:45
1
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15% (low)

Question Stats:

89% (01:24) correct 11% (02:07) wrong based on 90 sessions

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

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

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

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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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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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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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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? &nbs [#permalink] 01 May 2017, 10:04
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# If 3^x – 3^(x – 1) =2(3^13), what is x?

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