换根公式推导过程高一的对数函数的里面有一个换底公式谁知道?请把那个推导过程发一下、、加上一定的需要的讲解、谢谢了!打错了

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)