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11 Mar 2014, 02:57
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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82% (01:38) correct
18%
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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
11 Mar 2014, 02:58
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SOLUTION
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
\((12^x)(4^{2x+ 1})= (2^k)(3^2)\);
\((2^{2x}*3^x)(2^{2(2x+ 1)})= (2^k)(3^2)\);
\((2^{2x+2(2x+ 1)}*3^x)= (2^k)(3^2)\);
Equate the powers of 3 --> \(x=2\);
Equate the powers of 2 --> \(2x+2(2x+ 1)=k\) --> \(6x+2=k\) --> \(k=14\).
Answer: E.
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
\((12^x)(4^{2x+ 1})= (2^k)(3^2)\);
\((2^{2x}*3^x)(2^{2(2x+ 1)})= (2^k)(3^2)\);
\((2^{2x+2(2x+ 1)}*3^x)= (2^k)(3^2)\);
Equate the powers of 3 --> \(x=2\);
Equate the powers of 2 --> \(2x+2(2x+ 1)=k\) --> \(6x+2=k\) --> \(k=14\).
Answer: E.
11 Mar 2014, 20:11
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Answer = (E) 14
Re-write as
\(3^x . 4^x . 4^{(2x+1)} = 2^k. 3^2\)
LHS & RHS has only 1 base of 3, so x = 2
\(4^2 . 4^5 = 2^k\)
\(4^7 = 2^k\)
K = 14
Re-write as
\(3^x . 4^x . 4^{(2x+1)} = 2^k. 3^2\)
LHS & RHS has only 1 base of 3, so x = 2
\(4^2 . 4^5 = 2^k\)
\(4^7 = 2^k\)
K = 14
\(thank you ^ {1000}\) 
[color=#ff0000] where do you see power of 3 ? 
