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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
Joined: 15 Oct 2015
Posts: 323
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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Updated on: 15 Feb 2016, 07:20
2
00:00

Difficulty:

15% (low)

Question Stats:

81% (01:20) correct 19% (02:32) wrong based on 127 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

Originally posted by Ekland on 15 Feb 2016, 07:18.
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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Joined: 02 Sep 2009
Posts: 50002
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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Joined: 06 Nov 2014
Posts: 1883
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
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Re: If 3^(x+2) – 3^x = 6^3(3^7), what is the value of x ? &nbs [#permalink] 23 Oct 2017, 07:39
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