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

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)

GMAT assassins aren't born, they're made,
Rich

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.

--
Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: https://www.optimus-prep.com/gmat-on-demand-course

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

3^x(3^2-1)=3^7*3^3*2^3
3^x(2^3)=3^10*2^3
x=10
Answer A

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

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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.