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

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Director
Joined: 18 Jul 2018
Posts: 503
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
If 3^(x+7) = 3^(x+4) + 78, then the value of x is  [#permalink]

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Updated on: 31 Jul 2018, 23:25
00:00

Difficulty:

35% (medium)

Question Stats:

65% (02:21) correct 35% (02:04) wrong based on 17 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

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Originally posted by Afc0892 on 31 Jul 2018, 22:25.
Last edited by Bunuel on 31 Jul 2018, 23:25, edited 2 times in total.
Renamed the topic and edited the question.
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3327
Location: India
GPA: 3.12
If 3^(x+7) = 3^(x+4) + 78, then the value of x is  [#permalink]

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31 Jul 2018, 22:37
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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Director
Joined: 18 Jul 2018
Posts: 503
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: If 3^(x+7) = 3^(x+4) + 78, then the value of x is  [#permalink]

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31 Jul 2018, 22:41
pushpitkc wrote:
The answer options in GMAT PS questions are always arranged in ascending order.

Will take care next time.
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Joined: 18 Jun 2018
Posts: 254
Re: If 3^(x+7) = 3^(x+4) + 78, then the value of x is  [#permalink]

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31 Jul 2018, 22:45
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, 22:45
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# If 3^(x+7) = 3^(x+4) + 78, then the value of x is

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