log2(3x-1)-log2(4-x)=4-log2(x-1)

log2(3x-1)-log2(4-x)=4-log2(x-1).......................................ОДЗ:{3x-1>0; 3x>1; x>1/3{4-x>0; -x>-4; x<4{x-1>0; x>1Решение ОДЗ: x e (1;4)........................................log2(3x-1)-log2(4-x)=log2(16)-log2(x-1)log2[(3x-1)/(4-x)] = log2[16/(x-1)](3x-1)/(4-x)= 16/(x-1)16(4-x)=(3x-1)(x-1)64-16x=3x^2-4x+164-16x-3x^2+4x-1=0-3x^2-12x+63=03x^2+12x-63=0 |:3x^2+4x-21=0D=4^2-4*1*(-21)=100x1=(-4-10)/2=-7 - не подходит по ОДЗx2=(-4+10)/2=3Ответ:3