设p,q满足log9p=log12q=log16(p+q),求q/p的值.注:

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/24 13:36:12
设p,q满足log9p=log12q=log16(p+q),求q/p的值.注:设p,q满足log9p=log12q=log16(p+q),求q/p的值.注:设p,q满足log9p=log12q=log

设p,q满足log9p=log12q=log16(p+q),求q/p的值.注:
设p,q满足log9p=log12q=log16(p+q),求q/p的值.注:

设p,q满足log9p=log12q=log16(p+q),求q/p的值.注:
log9(p)=log12(q)=log16(p q) lgp/(2lg3)=lgq/(2lg2 lg3)=lg(p q)/4lg2 [lgp lg(p q)]/(4lg2 2lg3)=lgq/(2lg2 lg3) lgp lg(p q)=2lgq lg(p^2 pq)=lg(q^2) p^2 pq-q^2=0 q^2-pq-p^2=0 q=p(1±√5)/2 q/p=(1±√5)/2