早教吧作业答案频道 -->数学-->
已知3^a=5^b=225,则1/a+1/b=?大哥大姐帮帮忙
题目详情
已知3^a=5^b=225,则1/a+1/b=?大哥大姐帮帮忙
▼优质解答
答案和解析
3^a=5^b=225,
则
a
=log(3,225)
=2+log(3,25)
=2+2*(lg5/lg3)
=2(lg5+lg3)/lg3,
b
=log(5,225)
=2+log(5,9)
=2+2*(lg3/lg5)
=2(lg5+lg3)/lg5,
所以
1/a+1/b
=(lg3+lg5)/[2(lg5+lg3)]
=1/2,
则
a
=log(3,225)
=2+log(3,25)
=2+2*(lg5/lg3)
=2(lg5+lg3)/lg3,
b
=log(5,225)
=2+log(5,9)
=2+2*(lg3/lg5)
=2(lg5+lg3)/lg5,
所以
1/a+1/b
=(lg3+lg5)/[2(lg5+lg3)]
=1/2,
看了 已知3^a=5^b=225,...的网友还看了以下：