Question

解方程2（log3x)^2+log3x-1=0

Answer 1

2（log3x)^2+log3x-1=0
(2log3x-1)(log3x+1)=0
2log3x-1=0
log3x=1/2
x=3^(1/2)
或log3x+1=0
log3x=-1
x=3^(-1)=1/3
即解是X=3^(1/2)和1/3.

Answer 2

设log3x=t
原式等于2t^2+t-1=0
（2t-1）*（t+1）=0
t=-1或t=0.5
将t代回，log3x=-1 log3x=0.5
3^-1=x 3^0.5=x
x=1/3