对数运算公式推导最好详细点.

由对数定义,若c=log(a)b c'=log(a)b'
则a^c=b a^c'=b'
a^(c+c')=a^c*a^c'=bb'
两边对a取对数
log(a)b+log(a)b'=log(a)bb'
任取另一个数d>0
b^(log(b)d)=d
(a^c)^log(b)d=d
a^(log(a)*log(b)d)=d
两边对a取对数,有
log(a)b*log(b)d=log(a)d
又任取另一数e>0
e^log(e)a=a
(e^log(e)a)^c=b
e(log(e)a*log(a)b)=b
两边对e取对数
log(e)a*log(a)b=log(e)b
特别的,当d=b^n,e=a^n,则a=e^(1/n),log(b)d=n,log(e)a=1/n
有log(a)b^n=n*log(a)b
log(a^n)b=1/n*log(a)