已知x>0,y>0,lg2x+lg8y=lg2,则1x+13y的最小值是( ) A.2 B.22 C.4 D.23
问题描述:
已知x>0,y>0,lg2x+lg8y=lg2,则
+1 x
的最小值是( )1 3y
A. 2
B. 2
2
C. 4
D. 2
3
答
∵lg2x+lg8y=lg2,∴lg(2x•8y)=lg2,∴2x+3y=2,∴x+3y=1.
∵x>0,y>0,∴
+1 x
=(x+3y)(1 3y
+1 x
)=2+1 3y
+3y x
≥2+2x 3y
=4,当且仅当x=3y=
•3y x
x 3y
时取等号.1 2
故选C.