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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
If 2^x - 2^(x - 2) = 3*2^13 what is the value of x?
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06 Feb 2023, 21:50
06 Feb 2023, 21:50
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Question Stats:
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If \(2^x-2^{(x-2)}=3*2^{13}\) what is the value of x?
A. 9
B. 11
C. 13
D. 15
E. 17
A. 9
B. 11
C. 13
D. 15
E. 17
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
Re: If 2^x - 2^(x - 2) = 3*2^13 what is the value of x?
[#permalink]
08 Feb 2023, 20:57
08 Feb 2023, 20:57
1
Expert Reply
One more method:
\(2^x - 2^{(x-2)} = 3 * 2^{13}\)
\(2^x - 2^{(x-2)} = ( 4-1 ) * 2^{13}\)
\(2^x - 2^{(x-2)} = 4 * 2^{13} - 1 * 2^{13}\)
\(2^x - 2^{(x-2)} = 2^{15} - 2^{13}\)
Comparing both sides, we get x = 15 = Answer = D
Answer: D
\(2^x - 2^{(x-2)} = 3 * 2^{13}\)
\(2^x - 2^{(x-2)} = ( 4-1 ) * 2^{13}\)
\(2^x - 2^{(x-2)} = 4 * 2^{13} - 1 * 2^{13}\)
\(2^x - 2^{(x-2)} = 2^{15} - 2^{13}\)
Comparing both sides, we get x = 15 = Answer = D
Answer: D
gmatclubot
Re: If 2^x - 2^(x - 2) = 3*2^13 what is the value of x? [#permalink]
08 Feb 2023, 20:57
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