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已知lg2=A,lg3=B,求log以3为底4的对数,log以2为底...

log(2)3=lg3/lg2 log(3)4=lg4/lg3 log(2)3-log(3)4=lg3/lg2-lg4/lg3=[(lg3)^2-lg2lg4]/(lg2lg3) 因为分母lg2lg3大于0.因此只要比较分子的正负就可以判断二个数的大小 又根据基本不等式,简单推导如下:若a,b是正数,则 [...

换底公式 原式=(lg3/lg4+lg3/lg8)×lg2/lg3 =(lg3/2lg2+lg3/3lg2)×lg2/lg3 =(1/2+1/3)×lg3/lg2×lg2/lg3 =5/6

log2(3)log3(4)+lg4+lg25 =2log2(3)log3(2)+lg100 =2+2=4

a=lg3/lg2 lg3=alg2 b=lg7/lg3 lg7=blg3=ablg2 log42(56) =lg56/lg42 =lg(2^3*7)/lg(2*3*7) =(3lg2+lg7)/(lg2+lg3+lg7) =(3lg2+ablg2)/(lg2+alg2+ablg2) =(3+ab)/(1+a+ab)

你参考看看~

log以2为底25的对数乘以以3为底4的对数乘以5为底9的对数 =lg25/lg2*lg4/lg3*lg9/lg5 =2lg5/lg2*2lg2/lg3*2lg3/lg5 =4lg5/lg3*2lg3/lg5 =8

log以4为底8的对数-log以9分之1为底3的对数-log以根号2为底4的对数 =lg8/lg4-lg3/lg(1/9)-lg4/lg(√2) =3lg2/2lg2-lg3/(-2)lg3-2lg2/(1/2)lg2 =3/2 +1/2-4 =-2

这个是近似值 lg2≈0.3010 lg3≈0.4771 lg4=2lg2≈0.6020 lg5=1-lg2≈0.6990

log以4为底3的对数×log以9为底2的对数-log以1/2为底32的四次方根的对数 =(lg3/lg4)*(lg2/lg9)-lg32的四次方根/lg(1/2) =(lg3/2lg2)*(lg2/2lg3)-(5/4)*lg2/(-lg2) =1/4+5/4 =3/2

(以四为底三的对数+以八为底三的对数)()以三为底二的对数+以九为底二的对数 中间那个括号里是乘号吧? =(lg3/lg4+lg3/lg8)xlg2/lg3+lg2/lg9) =[lg3/(2lg2)+lg3/(3lg2)]xlg2/lg3+lg2/(2lg3) =[3lg3/(6lg2)+2lg3/(6lg2)]xlg2/lg3+lg2/(2lg3) =[5...

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