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

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Senior Manager
Joined: 20 May 2014
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Kudos [?]: 49 [0], given: 220

If 3^(-x) + 3^(-x) + 3^(-x) = 1, what is the value of x? [#permalink]  05 Nov 2017, 23:25
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Question Stats:

100% (00:28) correct 0% (00:00) wrong based on 2 sessions
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

Kudos for correct solution.
[Reveal] Spoiler: OA
Director
Joined: 03 Sep 2017
Posts: 521
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Kudos [?]: 330 [1] , given: 66

Re: If 3^(-x) + 3^(-x) + 3^(-x) = 1, what is the value of x? [#permalink]  06 Nov 2017, 05:57
1
KUDOS
The expression above can be rewritten as $$3*3^{-x}=1$$.

Then, each number to the power of zero is equal to 1, thus we can rewrite 1 as 3^0 and we get $$3^{1-x}=3^0$$.

Finally, in order to have the two sides of the equation equal, it must be that the exponents are equal, i.e. $$1-x=0$$. From which we get x = 1.

Re: If 3^(-x) + 3^(-x) + 3^(-x) = 1, what is the value of x?   [#permalink] 06 Nov 2017, 05:57
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