Then (1-x)(x+3)= 1.

-x^2-2x+3= 1

x^2+2x-2=0

Domain,1-x >; 0，x+3 & gt； 0

-3 & lt； x & lt 1

So x=- 1+√2 or x=- 1-√2.

Loga(X) is a decreasing function.

The minimum value of f(x) is -4.

loga[( 1-x)(x+3)]& gt； =-4=loga(a^-4)

So (1-x) (x+3) < = a-4.

( 1-x)(x+3)=-x^2-2x+3=-(x+ 1)^2+4

So the maximum value of true number =4.

So a (-4) = 4.

a=4^(- 1/4)=√2/2