Question

若lgx,lg(3x-2),lg(3x+2)三个树成等差数列,则logx2被根号2是多少

Answer 1

2lg(3x-2)=lg(3x+2)+lgx

（3x-2)^2=3x^2+2x

9x^2-12x+4=3x^2+2x

6x^2-14x+4=0

3x^2-7x+2=0

(3x-1)(x-2)=0

x1=1/3 x2=2

当x1=1/3时 3x-2=-1舍去

x=2

logx2*根号2=log2(2)^(3/2)=3/2