解不等式:根号3log(a)(x)-2<2log(a)(x)-1

令m=3loga(x)-2
loga(x)=(m+2)/3
所以√m<2(m+2)/3-1
3√m<2m+1
2m-3√m+1>=0
(2√m-1)(√m-1)>=0
所以0<=√m<=1/2,√m>=1

0<=√m<=1/2
0<=m<=1/4
0<=3loga(x)-2<=1/4
2/3<=loga(x)<=3/4
若0<a<1,loga(x)是减函数
则a^(3/4)<=x<=a^(2/3)
若a>1,loga(x)是增函数
则a^(2/3)<=x<=a^(3/4)

√m>=1
m>=1
3loga(x)-2>=1
loga(x)>=1=loga(a)
a>1,则x>a
0<a<1,0<x<a

综上
0<a<1,0<x<a,a^(3/4)<=x<=a^(2/3)
a>1,a^(2/3)<=x<=a^(3/4),x>a