log(a)(b)=log(c)(b) /log(c)(a) 怎么证log(a)(b)=log(c)(b) /log(c)(a)怎么证

log(a)(b)=log(c)(b) /log(c)(a) 怎么证log(a)(b)=log(c)(b) /log(c)(a)怎么证
log(a)(b)=log(c)(b) /log(c)(a) 怎么证
log(a)(b)=log(c)(b) /log(c)(a)怎么证

log(a)(b)=log(c)(b) /log(c)(a) 怎么证log(a)(b)=log(c)(b) /log(c)(a)怎么证
若有对数log（a）（b）设a=n^x,b=n^y
则 log（a）（b）=log（n^x）(n^y)
根据 对数的基本公式
log(a）(M^n)=nloga(M) 和
基本公式
log(a^n)M=1/n×log(a) M
易得 log(n^x)(n^y)=y/x
由 a=n^x,b=n^y 可得 x=log(n)(a),y=log(n)(b)
则有：log(a)(b)=log(n^x)(n^y)=log(n)(b)/log(n)(a)
得证：log(a)(b)=log(n)(b)/log(n)(a)

b=a^[log(a)(b)]=c^[log(c)(b)]
a=c^[log(c)(a)]
所以 b={c^[log(c)a]}^[log(a)(b)]
=c^{[log(c)(a)]*[log(a)(b)]}
所以log(c)(b)]=[log(c)(a)]*[log(a)(b)]
所以log(a)(b)=log(c)(b) /log(c)(a)