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If 3^(-x)+3^(-x)+3^(-x)=1, what is the value of x?

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V
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If 3^(-x)+3^(-x)+3^(-x)=1, what is the value of x? [#permalink]

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New post 16 Aug 2017, 00:30
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E

Difficulty:

  15% (low)

Question Stats:

85% (00:31) correct 15% (00:33) wrong based on 120 sessions

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Kudos [?]: 129056 [0], given: 12187

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Re: If 3^(-x)+3^(-x)+3^(-x)=1, what is the value of x? [#permalink]

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New post 16 Aug 2017, 00:39
3(3^-x)=3^(1-x)=1
Implies x=1

Sent from my XT1706 using GMAT Club Forum mobile app

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GMAT 1: 640 Q48 V30
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Re: If 3^(-x)+3^(-x)+3^(-x)=1, what is the value of x? [#permalink]

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New post 16 Aug 2017, 01:49
3/3^x=1; 3^1-x=3^0; 1-x=0; 1=x

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Director
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If 3^(-x)+3^(-x)+3^(-x)=1, what is the value of x? [#permalink]

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New post 16 Aug 2017, 07:16
Bunuel wrote:
If \(3^{-x}+3^{-x}+3^{-x}=1\), what is the value of x?

A. -1

B. -1/2

C. 1/3

D. 1/2

E. 1

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

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

\(3^{-x}(3) = 1\)

\(3^{(-x+1)} = 1\) ----- (i)

\(3^0 = 1\), Therefore substituting \(3^0\) in equation (i) we get;

\(3^{(-x+1)} = 3^0\)

\(-x+1 = 0\)

\(x = 1\)

Answer (E)...

Kudos [?]: 303 [0], given: 261

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If 3^(-x)+3^(-x)+3^(-x)=1, what is the value of x? [#permalink]

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New post 16 Aug 2017, 07:24
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Bunuel wrote:
If \(3^{-x}+3^{-x}+3^{-x}=1\), what is the value of x?

A. -1

B. -1/2

C. 1/3

D. 1/2

E. 1

3\(^{-x}\) = \(\frac{1}{3^{x}}\)

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

\(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) = 1

x = 1

Answer E

Kudos [?]: 266 [1], given: 552

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Re: If 3^(-x)+3^(-x)+3^(-x)=1, what is the value of x? [#permalink]

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New post 22 Aug 2017, 08:27
X should be 1.
Inverse 3^-x and equate LHS & RHS using base and exponent concepts.
Option E.

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Re: If 3^(-x)+3^(-x)+3^(-x)=1, what is the value of x? [#permalink]

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New post 22 Aug 2017, 10:49
If 3−x+3−x+3−x=13−x+3−x+3−x=1, what is the value of x?

A. -1

B. -1/2

C. 1/3

D. 1/2

E. 1

=3/3^x=1
for this to be true only value of x can be 1, thus E is the correct answer.

Kudos [?]: 77 [0], given: 18

Re: If 3^(-x)+3^(-x)+3^(-x)=1, what is the value of x?   [#permalink] 22 Aug 2017, 10:49
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If 3^(-x)+3^(-x)+3^(-x)=1, what is the value of x?

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