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If x and k are integers and (12^x)(4^{2x+ 1})= (2^k)(3^2)
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05 Jun 2020, 08:36
05 Jun 2020, 08:36
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79% (01:21) correct
20% (02:21) wrong based on 68 sessions
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If x and k are integers and \((12^x)(4^{2x+ 1})= (2^k)(3^2)\), what is the value of k ?
(A) 5
(B) 7
(C) 10
(D) 12
(E) 14
(A) 5
(B) 7
(C) 10
(D) 12
(E) 14
Re: If x and k are integers and (12^x)(4^{2x+ 1})= (2^k)(3^2)
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05 Jun 2020, 08:36
05 Jun 2020, 08:36
Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
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Re: If x and k are integers and (12^x)(4^{2x+ 1})= (2^k)(3^2)
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05 Jun 2020, 09:52
05 Jun 2020, 09:52
Carcass wrote:
If x and k are integers and \((12^x)(4^{2x+ 1})= (2^k)(3^2)\), what is the value of k ?
(A) 5
(B) 7
(C) 10
(D) 12
(E) 14
(A) 5
(B) 7
(C) 10
(D) 12
(E) 14
Given: \((12^x)(4^{2x+ 1})= (2^k)(3^2)\)
Rewrite \(12\) and \(4\) as follows: \([(2^2)(3^1)]^x[(2^2)^{2x+ 1}]= (2^k)(3^2)\)
Apply exponent laws to get: \((2^{2x})(3^x)(2^{4x+ 2})= (2^k)(3^2)\)
On the left side, combine the powers of \(2\) to get: \((2^{6x+2})(3^x)= (2^k)(3^2)\)
At this point we can see that \(6x+2 = k\) AND \(x = 2\)
Take: \(6x+2 = k\)
Replace \(x\) with \(2\) to get: \(6(2)+2 = k\)
Evaluate: \(14 = k\)
Answer: E
Cheers,
Brent
