设x,y,Z∈R.5的x次方=9的y次方=225的z次方如题,则A.Z/1=X/1+Y/1B.Z/2=X/1+Y/1C.Z/1=X/2+Y/1D.Z/2=X/1+Y/2

Question

设x,y,Z∈R.5的x次方=9的y次方=225的z次方
如题,则
A.Z/1=X/1+Y/1 B.Z/2=X/1+Y/1 C.Z/1=X/2+Y/1 D.Z/2=X/1+Y/2

Answer 1

5^x=9^y=225^z ∴ 5^x=3^(2y)=15^(2z)=t
∴x=log5 (t) 2y=log3(t) 2z=log15(t)
∴1/x =logt (5) 1/(2y)=logt (3) 1/(2z)=logt(15)
∴1/x + 1/(2y) =1/(2z) 两边同乘以2有
2/x + 1/y =1/z 选择C