求对数解答题..证明,log(b)A=1/log(a)B

问题描述:

求对数解答题..
证明,
log(b)A=1/log(a)B

log(b)a=log(a)a/log(a)b
=1/log(a)b; {因为log(a)a=1}

用换底公式
log(B)A=log(C)B/log(C)A
log(A)B=log(C)A/log(C)B
所以log(B)A=1/log(A)B