题目

对数的证明啊
log a ^(m/n) = log a ^m - log a^ n
如何证明出来的
这个不是换底公式吧 你再看看呀

提问时间：2021-04-17

答案

换底公式
log(a)(N)=log(b)(N) / log(b)(a)
推导如下
N = a^[log(a)(N)]
a = b^[log(b)(a)]
综合两式可得
N = {b^[log(b)(a)]}^[log(a)(N)] = b^{[log(a)(N)]*[log(b)(a)]}
又因为N=b^[log(b)(N)]
所以
b^[log(b)(N)] = b^{[log(a)(N)]*[log(b)(a)]}
所以
log(b)(N) = [log(a)(N)]*[log(b)(a)] 所以log(a)(N)=log(b)(N) / log(b)(a)