log(9)(a)=log(15)(b)=log(25)(a+2b),求b比a的值
问题描述：
log(9)(a)=log(15)(b)=log(25)(a+2b),求b比a的值
log(9)(a)=log(15)(b)=log(25)(a+2b),其中9,15和25是底数
答
log(9)(a)=1/log(a)(9)=1/2{log(a)(3)}
log(9)(a)=log(15)(b)=log(25)(a+2b)=k
9^k=a,15^k=b
a+2b=25^k
9^k+2*15^k=25^k
(3/5)^k+2=(5/3)^k
(3/5)^k=y,(5/3)^k=1/y
y^2+2y+1=2
y=根号2-1或y=1-根号2(（3/5)k=根号2-1
k(lg3-lg5)=lg(根号2-1)
k=lg(根号2-1)/(lg3-lg5)....