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

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Senior Manager
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Concentration: Finance, Strategy
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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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15 Feb 2016, 07:18
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81% (00:53) correct 19% (02:26) wrong based on 88 sessions

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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.

Kudos [?]: 164 [1], given: 211

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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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15 Feb 2016, 07:25
Nez 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

$$3^{(x+2)} – 3^x = 6^3*3^7$$;

$$3^x(3^2 – 1) = (2*3)^3*3^7$$;

$$3^x*2^3 = 2^3*3^{10}$$;

$$x=10$$.

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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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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.

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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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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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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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