计算:log3 4·log4 5·log5 6…log80 81=

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/05 10:25:29
计算:log3 4·log4 5·log5 6…log80 81=

计算:log3 4·log4 5·log5 6…log80 81=
计算:log3 4·log4 5·log5 6…log80 81=

计算:log3 4·log4 5·log5 6…log80 81=
运用换底公式得:
原式=lg4/lg3 *lg5/lg4 *lg6/lg5 *...*lg81/lg80
=lg81/lg3
=4lg3/lg3
=4

log3 4·log4 5·log5 6…log80 81
= lg4/lg3 × lg5/lg4 × lg6/lg5 ×… × lg81/lg80
= lg81/lg3
= 4