求助TTGWD3-6

zyzwb

If x and k are integers and (12^x)(4^2x+1) = (2^k)(3²), what is the value of k?

 

A.     5

B.     7

C.     10

D.     12

E.      14

K是怎末求出来的呀?谢谢帮助:-)

yangjie8920

 (12^x)(4^2x+1) = (2^k)(3²)

等式左边划成: (2^2x3^x)(2^2(2x+1)) =>(2^6x+2) (3^x)=> 6x+2=K, 试算: x=1,2...

得x=2, k=14, 选E

不知对否?

irenaw

12^x=3^x*2^2x;  4^(2x+1)=2^(4x+2);  最后等式左边化为3^x*2^(6x+2);
由等式右边3^2得x=2, 把x=2代入6x+2=k, 得k=14

zyzwb

谢谢