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If 3^(x+7) = 3^(x+4) + 78, then the value of x is

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If 3^(x+7) = 3^(x+4) + 78, then the value of x is  [#permalink]

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New post Updated on: 01 Aug 2018, 00:25
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

63% (02:21) correct 38% (02:04) wrong based on 16 sessions

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If \(3^{x+7}=3^{x+4} + 78\), then the value of x is

A. 2
B. -2
C. 3
D. -3
E. 1

Originally posted by Afc0892 on 31 Jul 2018, 23:25.
Last edited by Bunuel on 01 Aug 2018, 00:25, edited 2 times in total.
Renamed the topic and edited the question.
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If 3^(x+7) = 3^(x+4) + 78, then the value of x is  [#permalink]

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New post 31 Jul 2018, 23:37
1
Afc0892 wrote:
If \(3^{x+7}\) = \(3^{x+4}\) + 78, then the value of x is

1) 2
2) -2
3) 3
4) -3
5) 1


\(3^{x+7}\) = \(3^{x+4}\) + 78 can be re-written as \(3^{x+7}\) - \(3^{x+4} = 78\)

\(78\) can be further broken down as \(81 - 3 = 3^4 - 3^1\)

On equating the common terms in both LHS and RHS, we have either x + 7 = 4 or x + 4 = 1.

In either cases, the value of x is always -3 (Option D)

Afc0892 - The answer options in GMAT PS questions are always arranged in ascending order.
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Re: If 3^(x+7) = 3^(x+4) + 78, then the value of x is  [#permalink]

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New post 31 Jul 2018, 23:41
pushpitkc wrote:
The answer options in GMAT PS questions are always arranged in ascending order.

Will take care next time.
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Re: If 3^(x+7) = 3^(x+4) + 78, then the value of x is  [#permalink]

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New post 31 Jul 2018, 23:45
Afc0892 wrote:
If \(3^{x+7}\) = \(3^{x+4}\) + 78, then the value of x is

1) 2
2) -2
3) 3
4) -3
5) 1


OA:D
\(3^{x+7}\) = \(3^{x+4} + 78\)

\(3^x3^7-3^x3^4=78\)

\(3^x(3^7-3^4)=78\)

\(3^x3^4(3^3-1)=78\)

\(3^x3^4(26)=78\)

\(3^x3^4 =\frac{78}{26}\)

\(3^{x+4} =3^1\)

\(x+4 =1\)

\(x=-3\)
Re: If 3^(x+7) = 3^(x+4) + 78, then the value of x is &nbs [#permalink] 31 Jul 2018, 23:45
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