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# If 3^x-3^{x-2}=648, x=?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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05 Sep 2017, 00:26
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25% (medium)

Question Stats:

83% (01:38) correct 17% (02:15) wrong based on 58 sessions

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[GMAT math practice question]

If $$3^x-3^{x-2}=648$$, x=?

A. 5
B. 6
C. 7
D. 8
E. 9

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 04 Dec 2015 Posts: 750 Location: India Concentration: Technology, Strategy WE: Information Technology (Consulting) Re: If 3^x-3^{x-2}=648, x=? [#permalink] ### Show Tags 05 Sep 2017, 00:36 1 MathRevolution wrote: [GMAT math practice question] If $$3^x-3^{x-2}=648$$, x=? A. 5 B. 6 C. 7 D. 8 E. 9 $$3^x-3^{x-2} = 648$$ $$3^x-\frac{3^x}{3^2} = 2^3*3^4$$ $$\frac{3^x*3^2-3^x}{3^2} = 2^3*3^4$$ $$3^x*3^2-3^x = 2^3*3^4 * 3^2$$ $$3^x(3^2-1) = 2^3*3^6$$ $$3^x(9-1) = 2^3*3^6$$ $$3^x(8) = 8*3^6$$ $$3^x = 3^6$$ $$x = 6$$ Answer (B)... _________________ Please Press "+1 Kudos" to appreciate. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7363 GMAT 1: 760 Q51 V42 GPA: 3.82 If 3^x-3^{x-2}=648, x=? [#permalink] ### Show Tags Updated on: 09 Sep 2017, 21:03 => $$3^x-3^{x-2} = 3^{x-2}3^2-3^{x-2} = 3^{x-2}(3^2-1) = 3^{x-2} 8 = 648$$ $$3^{x-2} = 81 = 3^4$$ $$x – 2 = 4$$ $$x = 6$$ Ans: B _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Originally posted by MathRevolution on 07 Sep 2017, 01:48.
Last edited by MathRevolution on 09 Sep 2017, 21:03, edited 1 time in total.
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07 Sep 2017, 16:49
[quote=]

If $$3^x-3^{x-2}=648$$, x=?

A. 5
B. 6
C. 7
D. 8
E. 9[/quote]

We can simplify the given equation:

3^x - (3^x)(3^-2) = 648

3^x(1 - 3^-2) = 648

3^x(1 - 1/9) = 648

3^x(8/9) = 648

3^x = 648 x 9/8

3^x = 9 x 81

3^x = 3^2 x 3^4

3^x = 3^6

x = 6

Alternate Solution:

Let’s write 3^x = 3^(x - 2) * 3^2. Then:

3^(x - 2) * 3^2 - 3^(x - 2) = 648

3^(x - 2)[3^2 - 1] = 648

3^(x - 2)[8] = 648

3^(x - 2) = 81 = 3^4

x - 2 = 4

x = 6

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Re: If 3^x-3^{x-2}=648, x=?   [#permalink] 07 Sep 2017, 16:49
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