- 指数与指数幂的运算
- 共1477题
不用计算器计算下列各式的值:
(1)(a23b12)(-3a12b13)÷(a16b56);
(2)log3+lg25+lg4-3log32.
正确答案
(1)原式=-9a23+12-16b12+13-56=-9ab0=-9a.
(2)原式=log33-12+lg(25×4)-2=-+2-2=-
.
已知9x-12•3x+27≤0,求y=(log2)•(log12
)最值及对应的x值.
正确答案
∵9x-12•3x+27≤0,∴(3x-3)•(3x-9)≤0,即3≤3x≤9,得1≤x≤2,
∴y=(log2x-1)(log 12212+log 122x)=(log2x-1)(log2x+)
∴令t=log2x,则0≤t≤1,
y=t2-t-
= (t-
1
4
)2-,
∴当t=1,即x=2时,y取得最大值0;
当t=,即x=
时,y取得最小值-
.
计算
(1)-
+(2
)-0.5-
π0
(2)log318-log32-log29•log34+2log23.
正确答案
(1)原式=|2-e|-+[(
)2]-12-
=e-2-+(
)-1-
=e-2-e+-
=-2.
(2)原式=log3-
×
+3
=log332-4+3
=2-4+3
=1.
计算:
(1)log256.25+lg0.01+ln-2 1+log23
(2)()-3+4×(
)-12×80.25-(-
)0.
正确答案
log256.25+lg0.01+ln- 21+log23
=log52.5-2+- 2log26
=log52.5-2+-6
=log52.5-
(2)(
1
2
)-3+4×(
16
49
)-12×80.25-(-
5
8
)0
=8+4××234-1
=7+7×234
计算:
(Ⅰ)2-12++
-
(Ⅱ)2×(lg)2+
lg2×lg5+
.
正确答案
(Ⅰ)2-12++
-
=+
+
+1-1
=2.
(Ⅱ)2×(lg)2+
lg2×lg5+
=2×(lg2)2+
lg2•lg5+
=lg22+
lg2•lg5-(lg
-1)
=lg22+
lg2•lg5-
g2+1
=lg2(lg2+lg5-1)+1
=lg2(lg10-1)+1
=1.
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