log以9为底4的对数

log2(25)*log3(1/16)*log5(1/9)=[2log2(5)]*[-4log3(2)]*[-2log5(3)=[2*lg5/lg2]*[-4*lg2/lg3]*[-2*lg3/lg5

即lg4/lg3*lg8/lg4*lgm/lg8=lg16/lg4lgm/lg3=2lg4/lg4=2lgm=2lg3=lg3²所以m=9

[log9(4)+log3(8)]/log1/3(16)=[lg4/lg9+lg8/lg3]/[lg16/lg1/3]=[2lg2/2lg3+3lg2/lg3]/[4lg2/(-lg3)]=4lg2/

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/(

=(lg3/lg4+;g3/lg8)(lg2/lg3+lg2/lg9)=(lg3/2lg2+;g3/3lg2)(lg2/lg3+lg2/2lg3)=(1/2+1/3)*lg3/lg2*(1+1/2)*

换底公式我喜欢ln所以log2(9)=ln9/ln2=ln(3^2)/ln2=2*ln3/ln2log3(4)=ln4/ln3=ln(2^2)/ln3=2*ln2/ln3log2(9)*log3(4)

9.

log2(25)*log3(4)*log5(9)=lg25/lg2*lg4/lg3*lg9/lg5(换底公式)=lg5^2/lg2*lg2^2/lg3*lg3^2/lg5=2lg5/lg2*2lg2/

8再问：是不是换成分数形式可以互相约掉再答：log2(25)*log3(4)*log5(9)=lg25*lg4*lg9/lg2*lg3*lg4=log2(4)*log3(9)*log5(25)=2*2

log2(25)*log3(4)*log5(9)=lg25/lg2*lg4/lg3*lg9/lg5(换底公式)=lg5^2/lg2*lg2^2/lg3*lg3^2/lg5=2lg5/lg2*2lg2/

解；可以利用换底公式,变为相同的底数来计算原式=(log以2为底3为真数÷log以2为底4为真数)×(log以2为底2为真数÷log以2为底9为真数)×(log以2为底4√32为真数÷log以2为底1

楼上写错了[log(3,2)+log(9,2)]*[log(4,3)+log(8.3)]=[log(3,2)+1/2log(3,2)]*[1/2log(2,3)+1/3log(2,3)]=3/2log

具体过程都在这儿了,自己看吧!

换底公式原式=(lg3/lg4+lg3/lg8)(lg2/lg3+lg2/lg9)=(lg3/2lg2+lg3/3lg2)(lg2/lg3+lg2/2lg3)=(lg3/lg2)(1/2+1/3)*(

log以3为底的4的对数/log以9为底的8的对数=log以3为底的2^2的对数/log以3^2为底的2^3的对数=log3(2^2)/log3^2(2^3)=4/3再问：最后一步在详细点再答：log

换底公式：log以3为底12+log以9为底36-log以27为底512的对数=lg12/lg3+lg36/lg9-lg512/lg27=（2lg2+lg3)/lg3+(lg2+lg3)/lg3-3l

解题思路：本题柱考察学生对于对数的运算的理解和应用。解题过程：

[log(5)(根号2)*log(7)9]/[log(5)(1/3)*log(5)(4的立方根)]={[lg(根号2)/lg5]*(lg9/lg7)}/{[lg(1/3)/lg5]*[lg4的立方根/

利用：log(a^n)[b^m]=(m/n)log(a)[b]则：log(3)[2]=log(3²)[2²]=log(9)[4]