问题 填空题

(log52+log252)(log25+log85)=______.

答案

(log52+log252)(log25+log85)

=(

lg2
lg5
+
lg2
2lg5
)(
lg5
lg2
+
lg5
3lg2
)

=

3lg2
2lg5
×
4lg5
3lg2
=2.

故答案为2.

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