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18 Aug 2010, 21:49
Kudos
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
78% (01:18) correct
22%
(01:38)
wrong
based on 18
sessions
History
Date
Time
Result
Not Attempted Yet
Hey everyone,
I hope you guys understand this one. I couldn't figure out how to display exponents. Thanks!
If (2 to the x) - (2 to the (x-2)) = 3 (2 to the 13), what is the value of x?
A. 9
B. 11
C. 13
D. 15
E. 17
I hope you guys understand this one. I couldn't figure out how to display exponents. Thanks!
If (2 to the x) - (2 to the (x-2)) = 3 (2 to the 13), what is the value of x?
A. 9
B. 11
C. 13
D. 15
E. 17
Archived Topic
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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
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18 Aug 2010, 23:20
Kudos
Bookmarks
Hi,
I am guessing the question is:
(2 to the power x) - (2 to the power (x-2)) = 3 (2 to the power 13)
2^x - 2^(x-2) = 3. 2^13
2^x - ((2^x) / (2^2)) = 3. 2^13
2^x [1 - (1/4)] = 3. 2^13
2^x [3/4] = 3. 2^13
2^(x-2) times 3 = 3. 2^13
3 times 2^(x-2) = 3 times 2^13
Hence, x-2 = 13; x = 15.
Hope this helps. Thanks.
I am guessing the question is:
(2 to the power x) - (2 to the power (x-2)) = 3 (2 to the power 13)
2^x - 2^(x-2) = 3. 2^13
2^x - ((2^x) / (2^2)) = 3. 2^13
2^x [1 - (1/4)] = 3. 2^13
2^x [3/4] = 3. 2^13
2^(x-2) times 3 = 3. 2^13
3 times 2^(x-2) = 3 times 2^13
Hence, x-2 = 13; x = 15.
Hope this helps. Thanks.
19 Aug 2010, 15:26
Kudos
Bookmarks
I got this question on GMATPrep the other day. I just worked it out real quick using the real numbers. I only did this because for some reason memorized the powers of 2 really high when I was a kid. If it had been another other number I would have had to work it out properly.
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
\(2^x-2^{x-2} = 3(2^{13})\)
\(2^x(1-2^{-2}) = 3(2^{13})\) Factor out \(2^x\)
\(2^x(1-1/4) = 3(2^{13})\) Convert \(2^{-2} = 1/4\)
\(2^x(3/4) = 3(2^{13})\) Subtract
\(2^x = (4/3)(3)(2^{13})\) Multiply both sides by 4/3
\(2^x = (4)(2^{13})\) Cancel
\(2^x = (2^2)(2^{13})\) Convert 4 to power of 2
\(2^x = 2^{13+2}\) Multiplication of power with same base
\(2^x = 2^{15}\) Simplify
\(x = 15\) Common base of 2 on both sides, drop the base and just work with the exponents.
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
\(2^x-2^{x-2} = 3(2^{13})\)
\(2^x(1-2^{-2}) = 3(2^{13})\) Factor out \(2^x\)
\(2^x(1-1/4) = 3(2^{13})\) Convert \(2^{-2} = 1/4\)
\(2^x(3/4) = 3(2^{13})\) Subtract
\(2^x = (4/3)(3)(2^{13})\) Multiply both sides by 4/3
\(2^x = (4)(2^{13})\) Cancel
\(2^x = (2^2)(2^{13})\) Convert 4 to power of 2
\(2^x = 2^{13+2}\) Multiplication of power with same base
\(2^x = 2^{15}\) Simplify
\(x = 15\) Common base of 2 on both sides, drop the base and just work with the exponents.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
