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

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Math Expert
Joined: 02 Sep 2009
Posts: 54696
If 3^(-x)+3^(-x)+3^(-x)=1, what is the value of x?  [#permalink]

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16 Aug 2017, 00:30
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Question Stats:

83% (00:44) correct 17% (01:13) wrong based on 153 sessions

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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

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Joined: 02 Jul 2017
Posts: 10
Re: If 3^(-x)+3^(-x)+3^(-x)=1, what is the value of x?  [#permalink]

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

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

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16 Aug 2017, 01:49
3/3^x=1; 3^1-x=3^0; 1-x=0; 1=x
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If 3^(-x)+3^(-x)+3^(-x)=1, what is the value of x?  [#permalink]

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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;

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

$$-x+1 = 0$$

$$x = 1$$

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

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16 Aug 2017, 07:24
1
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

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

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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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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.
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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