设lg2=a,lg3=b,那么lg1.8=______.
问题描述:
设lg2=a,lg3=b,那么lg
=______.
1.8
答
lg
=
1.8
lg1.8=1 2
lg1 2
=18 10
lg1 2
2×9 10
=
(lg 2+lg 9-1)1 2
=
(lg2+2lg3−1)1 2
=
(a+2b-1).1 2
故答案为
.a+2b−1 2
答案解析:利用对数的运算法则即可把原式化为 lg
=
1.8
lg 1.8=1 2
lg 1 2
=18 10
lg1 2
=2×9 10
(lg 2+lg 9-1),把已知代入即可.1 2
考试点:对数的运算性质.
知识点:熟练掌握对数的运算法则是解题的关键.