设p,q满足log9(p)=log12(q)=log16(p+q),求q/p的值

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设p,q满足log9(p)=log12(q)=log16(p+q),求q/p的值设p,q满足log9(p)=log12(q)=log16(p+q),求q/p的值设p,q满足log9(p)=log12(

设p,q满足log9(p)=log12(q)=log16(p+q),求q/p的值
设p,q满足log9(p)=log12(q)=log16(p+q),求q/p的值

设p,q满足log9(p)=log12(q)=log16(p+q),求q/p的值
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