数学不等式问题
1.已知a>2,求证log以a-1为底a的对数大于log以a为底a+1的对数2.log以a为底2的对数小于log以b为底2的对数小于0,则A.o<a<b<1B.0<b<a...
1.已知a>2,求证log以a-1为底a的对数大于log以a为底a+1的对数
2.log以a为底2的对数小于log以b为底2的对数小于0,则
A.o<a<b<1 B.0<b<a<1 C.a>b>1 D.b>a>1
3.某企业一年购买货物400t,每次购买x吨,运费每次4万元,一年总存储费4x万元,要使一年总运费与一年的总存储费用之和最小,则x=? 展开
2.log以a为底2的对数小于log以b为底2的对数小于0,则
A.o<a<b<1 B.0<b<a<1 C.a>b>1 D.b>a>1
3.某企业一年购买货物400t,每次购买x吨,运费每次4万元,一年总存储费4x万元,要使一年总运费与一年的总存储费用之和最小,则x=? 展开
2个回答
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1. 求证 log(a-1) a >loga (a+1)
a>2 log(a-1) a >0 loga (a+1)>0
log(a-1) a =1/loga (a-1)
要证 log(a-1) a >loga (a+1)
只需1/loga (a-1) >loga (a+1)
只需 【loga (a+1)】*【loga (a-1)】<1
需 【loga (a+1)】*【loga (a-1)】<=[loga (a+1)+loga (a-1)]^2/4
<=[loga(a^2-1)]^2/4<[loga a^2]^2/4=1
log(a-1) a >loga (a+1)
2. loga 2=1/log2 a
logb 2=1/log2 b
log以a为底2的对数小于log以b为底2的对数小于0,
loga 2<logb 2<0
1/log2 a<1/log2 b<0
log2 b<log2 a<0=log2 1 0<b<a<1
3. 总运费 (400/x)*4
总存储费用 4x
之和 y=1600/x+4x
>=2√(1600/x*4x)
=160
1600/x=4x x=20
a>2 log(a-1) a >0 loga (a+1)>0
log(a-1) a =1/loga (a-1)
要证 log(a-1) a >loga (a+1)
只需1/loga (a-1) >loga (a+1)
只需 【loga (a+1)】*【loga (a-1)】<1
需 【loga (a+1)】*【loga (a-1)】<=[loga (a+1)+loga (a-1)]^2/4
<=[loga(a^2-1)]^2/4<[loga a^2]^2/4=1
log(a-1) a >loga (a+1)
2. loga 2=1/log2 a
logb 2=1/log2 b
log以a为底2的对数小于log以b为底2的对数小于0,
loga 2<logb 2<0
1/log2 a<1/log2 b<0
log2 b<log2 a<0=log2 1 0<b<a<1
3. 总运费 (400/x)*4
总存储费用 4x
之和 y=1600/x+4x
>=2√(1600/x*4x)
=160
1600/x=4x x=20
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