[問題]天山 09-06

[GMAT]

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

答案:14

請問這要怎解?

[clbb]

(12^x)(4^2x+1)

=(4^x*3^x)[4^(2x+1)]

=(3^x)[4^(3x+1)]

=(3^x)[(2^2)^(3x+1)]

=(3^x)[2^(6x+2)]=(3^2)(2^k)

所以x=2, 6x+2=k =>k=14

[GMAT]

(12^x)(4^2x+1)

=(4^x*3^x)[4^(2x+1)]

=(3^x)[4^(3x+1)]

=(3^x)[(2^2)^(3x+1)]

=(3^x)[2^(6x+2)]=(3^2)(2^k)

所以x=2, 6x+2=k =>k=14

我懂了 謝謝!