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>1 Решение 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+1 64-16x-3x^2+4x-1=0 -3x^2-12x+63=0 3x^2+12x-63=0 |:3 x^2+4x-21=0 D=4^2-4*1*(-21)=100 x1=(-4-10)/2=-7 - не подходит по ОДЗ x2=(-4+10)/2=3 Ответ:3