计算log2(25)×log3(2√2)×log5(9)的结果为 2,3,5是底数

题目

计算log2(25)×log3(2√2)×log5(9)的结果为 2,3,5是底数

答案

log2(25)×log3(2√2)×log5(9) =log2(52)×log3[(2)^(3/2)]×log5(32) =2log2(5)×3/2log3(2)×2log5(3) =2×3/2×2×log2(5)×[log5(2)/log5(3)]×log5(3) =6 log2(5)×log5(2) =6log2(2) =6