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If 3^(x+2) – 3^x = 6^3(3^7), what is the value of x ?

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If 3^(x+2) – 3^x = 6^3(3^7), what is the value of x ? [#permalink]

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If \(3^{(x+2)} – 3^x = 6^3(3^7)\), what is the value of x ?

A. 10
B. 11
C. 12
D. 13
E. 14
[Reveal] Spoiler: OA

Last edited by Bunuel on 15 Feb 2016, 07:20, edited 2 times in total.
Renamed the topic and edited the question.

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If 3^(x+2) – 3^x = 6^3(3^7), what is the value of x ? [#permalink]

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New post 15 Feb 2016, 07:25

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Re: If 3^(x+2) – 3^x = 6^3(3^7), what is the value of x ? [#permalink]

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New post 14 Jun 2016, 00:27
Nezdem wrote:
If \(3^{(x+2)} – 3^x = 6^3(3^7)\), what is the value of x ?

A. 10
B. 11
C. 12
D. 13
E. 14


\(3^{(x+2)} – 3^x = 6^3(3^7)\)

\(3^{(x+2)} – 3^x\)
= \(3^x\)*(\(3^2\)-1) =\(3^x\)*8 = \(3^x\)*\(2^3\)

\((6^3)*(3^7)\) = \((2^3) * (3^3) * (3^7)\) = \((2^3) * (3^{10})\)

Comparing the two colour shaded expressions, we can say that x = 10.

A is the answer.

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If 3^(x+2) – 3^x = 6^3(3^7), what is the value of x ? [#permalink]

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New post 14 Jun 2016, 01:49
AbdurRakib wrote:
If \(3^{x+2 }-3^x=6^3*3^7\), what is the value of x ?

A.10
B.11
C.12
D.13
E.14


\(3^{x+2 }-3^x=6^3*3^7\)
\(3^x (9 - 1) = 2^3*3^3*3^7\)
\(3^x*8 = 8*3^{10}\)
\(3^x = 3^{10}\)
Hence x = 10

Correct Option: A
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Re: If 3^(x+2) – 3^x = 6^3(3^7), what is the value of x ? [#permalink]

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New post 23 Oct 2017, 07:39
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If 3^(x+2) – 3^x = 6^3(3^7), what is the value of x ?   [#permalink] 23 Oct 2017, 07:39
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