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

\(thank you ^ {1000}\)