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If 2^k + 2^(k-2) + 2^(k-3) = 2^(2k)*3^m, what is the value o
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21 Apr 2020, 09:40
21 Apr 2020, 09:40
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Question Stats:
64% (02:24) correct
35% (02:14) wrong based on 42 sessions
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If \(2^k + 2^{k-2} - 2^{k-3} = 2^{2k}*3^m\), what is the value of k+m?
A. -1
B. 0
C. 1
D. 2
E. 3
A. -1
B. 0
C. 1
D. 2
E. 3
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If 2^k + 2^(k-2) + 2^(k-3) = 2^(2k)*3^m, what is the value o
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21 Apr 2020, 09:47
21 Apr 2020, 09:47
2
Carcass wrote:
If \(2^k + 2^{k-2} - 2^{k-3} = 2^{2k}*3^m\), what is the value of k+m?
A. -1
B. 0
C. 1
D. 2
E. 3
A. -1
B. 0
C. 1
D. 2
E. 3
Given: \(2^k + 2^{k-2} - 2^{k-3} = 2^{2k}*3^m\)
Factor to get: \(2^{k-3}(2^3 + 2^1 - 1) = 2^{2k}*3^m\)
Evaluate: \(2^{k-3}(9) = 2^{2k}*3^m\)
Rewrite \(9\) as a power of \(3\) to get: \(2^{k-3}(3^2) = 2^{2k}*3^m\)
We can now conclude two things: \(2^{k-3}= 2^{2k}\) and \(3^2 = 3^m\)
If \(2^{k-3}= 2^{2k}\), then \(k-3= 2k\), which means \(k = -3\)
If \(3^2 = 3^m\), then \(m = 2\)
So, \(k+m = (-3) + 2 = -1\)
Answer: A
Cheers,
Brent
Re: If 2^k + 2^(k-2) + 2^(k-3) = 2^(2k)*3^m, what is the value o
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02 Sep 2024, 09:15
02 Sep 2024, 09:15
Hello from the GRE Prep Club BumpBot!
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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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).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
