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if 3^x+3^x+3^x=3^21, what is x
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06 Mar 2021, 06:46
06 Mar 2021, 06:46
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If \(3^x+3^x+3^x=3^{21}\), what is x?
(A) 1
(B) 3
(C) 7
(D) 20
(E) 21
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
(A) 1
(B) 3
(C) 7
(D) 20
(E) 21
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Posts: 6218
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Re: if 3^x+3^x+3^x=3^21, what is x
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06 Mar 2021, 07:08
06 Mar 2021, 07:08
2
Carcass wrote:
If \(3^x+3^x+3^x=3^{21}\), what is x?
(A) 1
(B) 3
(C) 7
(D) 20
(E) 21
(A) 1
(B) 3
(C) 7
(D) 20
(E) 21
ASIDE-----------------------------
Notice the following:
k + k + k = 3k
w² + w² + w² = 3w²
xy + xy + xy = 3xy
Likewise, 3^x + 3^x + 3^x = 3(3^x)
-------------------------------------
Now let's answer the question....
Given: \(3^x+3^x+3^x=3^{21}\)
Simplify left side: \(3(3^x)=3^{21}\)
Rewrite the first \(3\) as follows: \((3^1)(3^x)=3^{21}\)
Apply the Product Law to simplify the left side: \(3^{x+1}=3^{21}\)
Now that we have the same base on both sides, we can conclude that the exponents are equal: \(x+1 = 21\)
Solve to get: \(x = 20\)
Answer: D
Cheers,
Brent
Re: if 3^x+3^x+3^x=3^21, what is x
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17 Feb 2024, 15:11
17 Feb 2024, 15:11
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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