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If x and k are integers and (12^x) = (2^k)(3^2), what is the

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If x and k are integers and (12^x) = (2^k)(3^2), what is the [#permalink] New post 02 Jan 2006, 21:56
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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
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JAI HIND!

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Re: PS: Exponents [#permalink] New post 02 Jan 2006, 22:25
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JAI HIND 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

(12^x)[4^(2x+1)] = (2^k)(3^2)
[(3x4)^x] 2^2(2x+1) = (2^k)(3^2)
(3^x) (4^x) 2^(4x+2) = (2^k)(3^2)
(3^x) (2^2x) 2^(4x+2) = (2^k)(3^2)
(3^x) 2^(2x+4x+2) = (2^k)(3^2)
(3^x) 2^(6x+2) = (2^k)(3^2)
(3^x) 2^(6x+2) = (2^k)(3^2)

now, x=2

6x+2 = k
k = 14
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 [#permalink] New post 02 Jan 2006, 23:27
(12^x)[4^(2x+1)]
= (12^x)(4^2x)(4)
= (4^x)(3^x)(4^2x)(4)
= (4^3x+1)(3^x)
= (2^6x+2)(3^x)

x = 2
k = 6x+2 = 14

Ans E
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 [#permalink] New post 04 Jan 2006, 02:02
Thanks guys! OA is 14.
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Re: If x and k are integers and (12^x) = (2^k)(3^2), what is the [#permalink] New post 03 Feb 2016, 08:22
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Re: If x and k are integers and (12^x) = (2^k)(3^2), what is the   [#permalink] 03 Feb 2016, 08:22
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