设a>b>1,log(a)b+log(b)a=10/3,则log(a)b-log(b)a=

问题描述:

设a>b>1,log(a)b+log(b)a=10/3,则log(a)b-log(b)a=

即lgb/lga+lga/lgb=10/3
令x=lgb/lga
则x+1/x=10/3
3x²-10x+3=0
x=3,x=1/3
因为a>b>1
所以0