计算:log_5 35+2log_1/2 根号2-log_5 1/50-log_5 14

题目

计算:log_5 35+2log_1/2 根号2-log_5 1/50-log_5 14
注意:log_后面的数均为底数

答案

log5(35)+2log1/2(√2)-log5(1/50)-log5(14)
=log5(35)-log5(1/50)-log5(14)+2log1/2(√2)
=log5(35×50×(1/14))+2×(1/2)log1/2(2)
=log5(5^3)+log1/2((1/2^(-1))
=3-1
=2