解关于x的不等式 log2(x-1)>log4[a(x-2)+1] (a>1).

定义域
x-1>0,x>1
a(x-2)+1>0
x-2>-1/a
x>2-1/a
a>1
0<1/a<1
所以1<2-1/a<2
所以定义域x>2-1/a
log4N=lgN/lg4=lgN/2lg2=(1/2)log2N
所以不等式是log2(x-1)>(1/2)log2[a(x-2)+1]
2log2(x-1)>log2[a(x-2)+1]
log2(x-1)^2>log2[a(x-2)+1]
(x-1)^2>a(x-2)+1
x^2-2x+1>ax-2a+1
x^2-(a+2)+2a>0
(x-2)(x-a)>0
若1则x>2,x则2-1/a2
若a=2
则(x-2)^2>0
x不等于2
若a>2
则2-1/aa