lg2 =a lg3 =b 表示log2 153^a=5^b=15 求1/a+1/b
问题描述：
lg2 =a lg3 =b 表示log2 15
3^a=5^b=15 求1/a+1/b
答
a=log3 15
b=log5 15
1/a+1/b=a+b/ab
=(log3 15 +log 5 15)/log3 15.log5 15
=(ln3/ln5+ln5/ln15)/(ln3/15 .ln5/ln15)
=(ln5+ln3)/ln15
=1
答
log2 15
=log2(3*5)
=log2 3+log2 5
=lg3/lg2+lg5/lg2
=b/a+(1-lg2)/lg2
=b/a+(1-a)/a