Log2 (3x-1) - log2 (4-x) = 4-log2 (x-1)

Log2 (3x-1) - log2 (4-x) = 4-log2 (x-1)

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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)

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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