问题 解答题
(Ⅰ)已知lg2=a,lg3=b,试用a,b表示log215;
(Ⅱ)化简求值:
6
1
4
+
[
3]82+0.027-
2
3
×(-
1
3
)-2
答案

(Ⅰ)log215=

lg15
lg2
=
lg3+lg5
lg2
=
lg3+lg
10
2
lg2
=
1+lg3-lg2
lg2

∵lg2=a,lg3=b,

log215=

1+lg3-lg2
lg2
=
1+b-a
a

(Ⅱ)

6
1
4
+
[3]
82+0.027-
2
3
×(-
1
3
)-2

=

(
5
2
)2
+
3
×82+((0.3)3)-
2
3
×(-3)2

=

5
2
+64
3
+
100
9
×9

=

205
2
+64
3

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