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If 9^(2x – 1) – 81^(x-1) = 1944, then x is

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Joined: 02 Sep 2009
Posts: 64246
If 9^(2x – 1) – 81^(x-1) = 1944, then x is  [#permalink]

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New post 02 Apr 2020, 09:42
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

67% (02:57) correct 33% (02:46) wrong based on 27 sessions

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GMAT Club Legend
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Joined: 11 Sep 2015
Posts: 4879
Location: Canada
GMAT 1: 770 Q49 V46
Re: If 9^(2x – 1) – 81^(x-1) = 1944, then x is  [#permalink]

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New post 02 Apr 2020, 09:50
Top Contributor
Bunuel wrote:
If \(9^{2x – 1} – 81^{x-1} = 1944\), then x is

A. 1/3
B. 4/9
C. 9/4
D. 3
E. 4


Given: \(9^{2x – 1} – 81^{x-1} = 1944\)

Rewrite \(81\) as follows: \(9^{2x – 1} – (9^2)^{x-1} = 1944\)

Apply the power of a power law to get: \(9^{2x – 1} – 9^{2x-2} = 1944\)

Factor to get: \(9^{2x-2}(9^1 - 1) = 1944\)

Simplify: \(9^{2x-2}(8) = 1944\)

Divide both sides by \(8\) to get: \(9^{2x-2} = 243\)

Rewrite \(9\) as follows: \((3^2)^{2x-2} = 243\)

Apply the power of a power law to get: \(3^{4x-4} = 3^5\)

Since we now have the same bases, we know that: \(4x-4 = 5\)

Which means: \(4x = 9\)

Solve: \(x = \frac{9}{4}\)

Answer: C

Cheers,
Brent
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Re: If 9^(2x – 1) – 81^(x-1) = 1944, then x is  [#permalink]

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New post 02 Apr 2020, 10:06
9^(2x – 1) – 81^(x-1) = 1944
or,9^(2x-1) – 9^(2x-2) = 1944
or,3^(4x)/9 – 3^(4x)/81 = 1944
or,8(3^(4x)/81) = 1944
or, x =9/4
correct answer is C
GMAT Club Bot
Re: If 9^(2x – 1) – 81^(x-1) = 1944, then x is   [#permalink] 02 Apr 2020, 10:06

If 9^(2x – 1) – 81^(x-1) = 1944, then x is

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