Question

已知a,b,c都是正数，且3^a=4^b=6^c，那么

A. 1/c=1/2+1/b B 2/c=2/a+1/b
C 1/c=2/a+2/b D 2/c=1/a+2/b
求答案 原因

Answer 1

答案 B
3^a=4^b=6^c
a*log(3)=b*log(4)=c*log(6)
a/b=log(4)/log(3)
a/c=log(6)/log(3)
2/c-2/a-1/b=(2*a/c-2-a/b)/a=(2*log(6)/log(3)-2-log(4)/log(3))/a
=(2*(log(2)+log(3))-2*log(3)-2*log(2))/(a*log(3))
=0/(a*log(3))
=0