Question

【急】!已知loga^2 x=logab y=logb^2(x+y)(a,b均为不等于1的正数,且ab不等于1）求x/y

Answer 1

loga^2 x=logab y=logb^2(x+y)=k

a^2k=x,(ab)^k=y,b^2k=x+y

x/y=a^2k/(ab)^k=(a/b)^k

a^2k+(ab)^k=b^2k

(a/b)^2k+(a/b)^k=1

[(a/b)^k+1/2]^2=5/4

x/y=(a/b)^k=（√5-1）/2