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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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New post 25 Feb 2015, 06:33
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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
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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 Updated on: 25 Feb 2015, 06:38
One step at a time...:

3^(x+2) –3^x = 6^3 (3^7)
3^(x+2) –3^x = 2^3 *3^3 *3^7
3^x (3^2-1) = 2^3* 3^3 *3^7
3^x* 2^3 = 2^3* 3^3* 3^7
3^x = (2^3*3^3*3^7) / 2^3
3^x = 3^10
x = 10

So, ANS A

Originally posted by pacifist85 on 25 Feb 2015, 06:37.
Last edited by pacifist85 on 25 Feb 2015, 06:38, edited 1 time in total.
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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 25 Feb 2015, 06:37
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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 25 Feb 2015, 22:58
Hi All,

This question involves Exponent rules and some Arithmetic. As pacifist85 and Bunuel have approached it, the "steps" are really just about re-organizing the values until you isolate the value of X. I'd likely approach it the same way under normal circumstances.

Here though, the answer choices ARE numbers, so one of them MUST be the value of X. If you're not comfortable with all of the necessary Exponent rules (in the abstract) just yet, then you can still get to the correct answer by TESTing THE ANSWERS.

I'm going to start with the "right side" of the equation, since it's all numbers:

(6^3)(3^7)

6^3 = (2^3)(3^3)

substituting that value in, we have....

(2^3)(3^3)(3^7) =
(8)(3^10)

So the "left side" must equal (8)(3^10)

Since we're dealing with (3^10), chances are that X isn't much bigger than maybe 10 or 11.

Let's TEST X = 11....

Plugging that into the "left-side", we get...

3^13 - 3^11

We can factor out 3^11, which gives us...

3^11(3^2 - 1) =
(3^11)(9-1) =
(3^11)(8)

This is close to what we're looking for, but is a little too BIG (we need (8)(3^10)), so X MUST be smaller. There's only one answer left...

Final Answer:

Here's the proof:

IF...X = 10

3^12 - 3^10 =
3^10(3^2 - 1)
(3^10)(9 - 1)
(3^10)(8)

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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 28 Feb 2015, 05:30
pacifist85 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

Given that 3^(x+2) –3^x=6^3(3^7)
So, 3^x[3^2 - 1] = 6^3 * 3^7
So, 3^x(8) = (2*3)^3 * 3^7
So, 3^x(8) = (2^3) * (3^3) (3^7)
So, 3^x(8) = 8 * 3^10
So, x = 10
Hence 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 03 Sep 2015, 00:37
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3^(x+2) -3^x=6^3(3^7)

or,3^x(3^2) -3^x =6^3(3^7)
or,3^x(3^2 -1)=6^3(3^7)
or,3^x=\(\frac{(6^3 3^7)}{8}\)
or,3^x=\(\frac{(2^3 3^3 3^7)}{2^3}\)
or,3^x=3^3 3^7
or,3^x =3^10
0r,x=10

So the Correct Answer is 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 03 Sep 2015, 00:48
Bunuel 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

Kudos for a correct solution.


3^x(3^2-1)=3^7*3^3*2^3
3^x(2^3)=3^10*2^3
x=10
Answer 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 14 Jul 2018, 19:16
pacifist85 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


First, let’s use the fact that 3^(x + 2) can be re-expressed as (3^x)(3^2). Simplifying the equation, we have:

(3^x)(3^2) - 3^x = (6^3)(3^7)

We factor 3^x from both terms of the left hand side of the equation, obtaining:

3^x(9 - 1) = (6^3)(3^7)

3^x(8) = (2^3)(3^3)(3^7)

3^x(8) = 8(3^10)

3^x = 3^10

x = 10

Answer: A
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Re: If 3^(x+2) – 3^x = (6^3)(3^7), what is the value of x? &nbs [#permalink] 14 Jul 2018, 19:16
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