问题 解答题
计算下列各式的值.
(1)lg12.5-lg
5
8
+lg
1
2

(2)2log510+log50.25;
(3)2log32-log3
32
9
+log38-3.
答案

(1)lg12.5-lg

5
8
+lg
1
2
=lg(12.5÷
5
8
×
1
2
)=lg10=1;

(2)2log510+log50.25=log5102+log50.25=log5(102×0.25)=log525=log552=2log55=2×1=2;

(3)2log32-log3

32
9
+log38-3

=2log32-(log332-log39)+log323-3

=2log32-log325+log332+3log32-3

=2log32-5log32+2+3log32-3

=-1.

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