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

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by Vincen » Wed Jul 22, 2020 12:40 pm

Timer

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Answers

A

B

C

D

E

Stats

Difficulty—

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

[spoiler]OA=E[/spoiler]

Source: Magoosh
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Re: If \(3^{-x}+3^{-x}+3^{-x}=1,\) what is the value of \(x?\)

by Jay@ManhattanReview » Wed Jul 22, 2020 11:10 pm
Vincen wrote: ↑
Wed Jul 22, 2020 12:40 pm
 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

[spoiler]OA=E[/spoiler]

Source: Magoosh
So, we have \(3^{-x}+3^{-x}+3^{-x}=1\)

\(3\times3^{-x}=1\)

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

=> -x + 1 = 0

x = 1

Correct answer: E

Hope this helps!

-Jay
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Re: If \(3^{-x}+3^{-x}+3^{-x}=1,\) what is the value of \(x?\)

by Scott@TargetTestPrep » Sat Jul 25, 2020 2:17 pm
Vincen wrote: ↑
Wed Jul 22, 2020 12:40 pm
 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

[spoiler]OA=E[/spoiler]

Solution:

We can simplify the given equation:

3^-x + 3^-x + 3^-x = 1

3^-x(3) = 1

3^-x = 1/3

3^-x = 3^-1

-x = -1

x = 1

Answer: E

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