Verified answer

1-x>0, 17-x-x^2>0;

-x>-1, x<1,

x^2+x-17<0,

x^2+x-17=0,

D=69,

x1=(-1-√69)/2≈-4,7; x2=(-1+√69)/2≈3,7;

(-1-√69)/2<x<(-1+√69)/2,

(-1-√69)/2<x<1,

x∈((-1-√69)/2;1);

log_3 (1-x) = log_3 (17-x-x^2),

1-x=17-x-x^2,

x^2-16=0,

(x+4)(x-4)=0,

x+4=0, x1=-4,

x-4=0, x2=4∉((-1-√69)/2;1),

x=-4.