Question

如何比较log(1/2)[2/3]和log(1/3)[1/2]的大小

Answer 1

log9x=(log3y)2 (log3y)2-1/2log3(x)=0 x=3y (log3y)2-1/2log3(3y)=0 (log3y)2-1/2log3(y)-1/2=0 2(log3y)2-log3(y)-1=0 [2log3(y)+1][log3(y)-1]=0 2log3(y)+1=0或log3(y)-1=0 log3(y)=-1/2或log3(y)=1 y=√3/3 或 y=1 2)x/y=k x=ky (log3y)2-1/2log3(ky)=0 2(log3y)2-log3(y)-log3(k)=0 2[log3(y)-1/4]^2-log3(k)-1/8=0 log3(k)=2[log3(y)-1/4]^2-1/8 当log3(y)=1/4时有最小值,y=3^(1/4) log3(k)=-1/8 k=3^(-1/8) 有最小值,3^(-1/8)