Question

a=log1/3 (1/2), b=log1/2(2/3), c=log3(4/3),比较a,b,c 的大小

Answer 1

由已知得a=log3(2),c=log3(4/3),从而得出a>c，明显易得b>c
5*a=5*log3(2)>log3(27)=3
5*b=5*log1/2(2/3)=5*log2(3/2)<log2(8)=3
所以a>0.6,b<0.6
所以a>b>c

Answer 2

a=log1/3(1/2)=log3(2)
b=log1/2(2/3)=log2(3/2)=log2(3)-1=1/log3(2)-1=1/a-1
c=log3(4/3)=log3(4)-1=2log3(2)-1=2a-1
∵1/2=log3(√3)<a<log3(3)=1
∴a-1<0
∴c<a