设x、y、z∈R，且5x=9y=225z，则（）A.1z=1x+1yB.2z=1x+1yC.1z=2x+1yD.2z=1x+2y

Question

设x、y、z∈R，且5^x=9^y=225^z，则（　　）
A. (1)/(z)=(1)/(x)+(1)/(y)
B. (2)/(z)=(1)/(x)+(1)/(y)
C. (1)/(z)=(2)/(x)+(1)/(y)
D. (2)/(z)=(1)/(x)+(2)/(y)

Answer 1

令5^x=9^y=225^z=t，
则x=log₅t，y=log₉t，z=log₂₂₅t，
∴(1)/(x)＝logt5，(1)/(y)＝logt9，(1)/(z)＝logt225，
∴(2)/(x)+(1)/(y)=2log_t5+log_t9=log_t25+log_t9=log_t225=(1)/(z)，
故选C．