求证loga b=1/logb a

题目

求证loga b=1/logb a

答案

由换底公式 log(a){b}=log(b){b}/log(b){a} ----取以b为底的对数 　　log(a){b}=1 =1/log(b){a} 还可变形得:log(a){b}×log(b){a}=1