Question

已知log a^2 x=log ab y =log b^2 (x+y) (a,b均为不等于1的正数且ab≠1) 是否可以

Answer 1

令loga^2(x)=logab(y)=logb^2(x+y)=t

则

x=a^(2t)

y=(ab)^t

x+y=b^(2t)

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

(a/b)^(2t)+(a/b)^t-1=0

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

(a/b)^t=(√5-1)/2或(a/b)^t=-(√5+1)/2(舍去)

x/y=a^(2t)/(ab)^t=(a/b)^t=（√5-1）/2