Bunuel wrote:
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.
Hi
Bunuel \((2^{2x+2(2x+ 1)}*3^x)= (2^k)(3^2)\);
after this \((2^{6x+2}*3^x)= (2^k)(3^2)\);
<--- i get this how do you Equate the powers of 3 --> \(x=2\); :?
where do you see power of 3 ? :? how you get 2 :? how do you Equate the powers of 2 --> \(2x+2(2x+ 1)=k\) --> \(6x+2=k\) --> \(k=14\).
and get 14 :? i know this rule -->
if \(a^x = a^y\) then \(x = y\)
in other words if the bases match then exponents are equal.
please explain
\(thank you ^ {1000}\)