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

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Joined: 02 Sep 2009
Posts: 64231
If 9^(2x – 1) – 81^(x-1) = 1944, then x is  [#permalink]

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02 Apr 2020, 09:42
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Difficulty:

35% (medium)

Question Stats:

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

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If $$9^{2x – 1} – 81^{x-1} = 1944$$, then x is

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

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Joined: 11 Sep 2015
Posts: 4877
GMAT 1: 770 Q49 V46
Re: If 9^(2x – 1) – 81^(x-1) = 1944, then x is  [#permalink]

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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: $$x = \frac{9}{4}$$

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

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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
Re: If 9^(2x – 1) – 81^(x-1) = 1944, then x is   [#permalink] 02 Apr 2020, 10:06