Question

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

如图，请写一下解题步骤，谢谢。

Answer 1

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<lgb<lga
lgb/lga=x<1
x=1/3

所以原式=1/3-3=-8/3

Answer 2

解：因为logab=lgb/lga logba=lga/lgb
于是令logab=lgb/lga =t
则3t+3/t=10

解得t=3或t=1/3(又a>b>1，故logab>1)
即t=3
因此log(a)(b)-log(b)(a)=t-1/t=3-1/3=8/3.