问题 解答题
(1)计算:
(log25)2-4log25+4
+log2
1
5

(2)(log43+log83)(log32+log92).
答案

(1)原式=

(log25-2)2
-log25=log25-2-log25=-2.

(2)原式=(

lg3
2lg2
+
lg3
3lg2
)(
lg2
lg3
+
lg2
2lg3
)=
lg3
lg2
lg2
lg3
(
1
2
+
1
3
)(1+
1
2
)
=
5
6
×
3
2
=
5
4

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