log以0.5为底的对数
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![log以0.5为底的对数](/uploads/image/f/672779-11-9.jpg?t=log%E4%BB%A50.5%E4%B8%BA%E5%BA%95%E7%9A%84%E5%AF%B9%E6%95%B0)
log2(25)*log3(1/16)*log5(1/9)=[2log2(5)]*[-4log3(2)]*[-2log5(3)=[2*lg5/lg2]*[-4*lg2/lg3]*[-2*lg3/lg5
两种写法:把平方写在log的右上角,或者,把平方写在整个对数加括号的右上角.已经是最简了,不能再化简了.
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/
为了书写方便,不妨记以a为底b的对数为:log【a】b(log【2】5+log【4】125)×[(log【3】2)/(log【√3】5)]=[(lg5)/(lg2)+(lg125)/(lg4)]×{[
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/(
log以3为底2的对数log以2为底3的对数>log以2为底2的对数=1>log以3为底2的对数
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/
(lg3/lg5)[(3lg5)/(3lg3)]=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: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
a+22log以5为底10的对数+log以5为底0.5的对数=log以5为底100的对数+log以5为底0.5的对数=log以5为底50的对数=log以5为底25的对数+log以5为底2的对数=2+a
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:
2log3(2)-log3(32/9)+log3(8)-5*2*log5(3)=log3(4)-log3(32/9)+log3(8)-5*2*log5(3)=log3(4/(32/9))+log3(8