Question

对数函数的换底公式怎么推导

就是logab=logcb/logca（a>0 a不等于1 c>0 c不等于1 b>0) 怎么推倒。

Answer 1

解：设p=log(a)b, q=log(c)a. 则：b=a^p, a=c^q
∴ b=a^p=(c^q)^p=c^(pq)
∴ pq=log(c)b, 即有：log(a)b*log(c)a=log(c)b
∴ log(a)b=logcb/logca

Answer 2

logc(b) =x , logc(a) =y
c^x=b, c^y=a => c=a^(1/y)
=> a^(x/y) = c^x = b
=> loga(b) = x/y