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

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Math Revolution GMAT Instructor
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If 3^x-3^{x-2}=648, x=? [#permalink]

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New post 05 Sep 2017, 00:26
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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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Re: If 3^x-3^{x-2}=648, x=? [#permalink]

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New post 05 Sep 2017, 00:36
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)...

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Math Revolution GMAT Instructor
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If 3^x-3^{x-2}=648, x=? [#permalink]

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New post 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
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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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Re: If 3^x-3^{x-2}=648, x=? [#permalink]

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New post 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

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