换底公式推导过程

题目

换底公式推导过程
1.log(a)(b)=1/log(b)(a)
2.log(a^n)(b^m)=m/n*[log(a)(b)]
3.log(a)(M^n)=nlog(a)(M)

答案

1.设log(a)(b)=N,则b=a^N,b^(-1)=a^(-N),b^[(-1)(-1/N)]=a,b^(1/N)=a,log(b)(a)=1/N,log(a)(b)=1/log(b)(a).2.设log(a^n)(b^m)=N,b^m=(a^n)^N=a^(nN),b=a^(nN/m),nN/m=log(a)(b),m/n*[log(a)(b)] =N=log(a^n)(b^m).3...