题目内容

(1)计算:0.064-
1
3
-(-
1
8
)0+7log72+0.25
5
2
×0.5-4

(2)已知a=lg2,10b=3,用a,b表示log6
30
(1)原式=(
64
1000
)
-
1
3
-1+2+(
1
4
)
5
2
× (
1
2
)
-4
=(
4
10
)
3×(-
1
3
)
-1+2+(
1
2
)
5
×(
1
2
)
-4
=
10
4
-1+2+
1
2
=4
        
(2)∵10b=3
∴b=lg3
又∵a=lg2
log6
30
=
1
2
log630=
1
2
(1+log65)
=
1
2
(1+
lg5
lg6
)=
1
2
(1+
lg
10
2
lg(2×3)
)= 
1
2
(1+
1-lg2
lg2+lg3
)
=
1
2
(1+
1-a
a+b
)=
b+1
2(a+b)
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