Объяснение:

1.

log8(16)=log2³(2⁴)=4/3•log2(2)=4/3

ответ: Б

2.

|8-4х|=6

8-4х=6 8-4х= -6

4х=8-6 4х=8+6

4х=2 4х=14

х=0,5 х=3,5

ответ: х1=0,5 ; х2=3,5

3.

|х²-5х|=6

х²-5х=6 х²-5х= -6

х²-5х-6=0 х²-5х+6=0

х²+х-6х-6=0 х²-2х-3х+6=0

х(х+1)-6(х+1)=0 х(х-2)-3(х-2)=0

(х+1)(х-6)=0 (х-2)(х-3)=0

х+1=0 х-6=0 х-2=0 х-3=0

х= -1 х=6 х=2 х=3

ответ: х1= -1 ; х2=2 ; х3=3 ; х4=6

Verified answer

1) Б

[tex] log_{8}(16) = log_{ {2}^{3} }( {2}^{4} ) = \frac{4}{3} [/tex]

2)

[tex] |8 - 4x| = 6 \\ 1) \: 8 - 4x = 6 \\ 4x = 8 - 6 \\ 4x = 2 \\ x = 2 \div 4 \\ x = 0.5 \\ 2) \: 8 - 4x = - 6 \\ 4x = 8 + 6 \\ 4x = 14 \\ x = 14 \div 4 \\ x = 3.5[/tex]

3)

[tex] | {x}^{2} - 5x | = 6 \\ 1) \: {x}^{2} - 5x = 6 \\ {x}^{2} - 5x - 6 = 0 \\ po \: \: teoreme \: \: vieta \\ {x}^{2} + bx + c = 0\\ x_{1} + x_{2} = - b\\ x_{1} x_{2} = c \\ \\ x_{1} + x_{2} = 5\\ x_{1} x_{2} = - 6\\ x_{1} = - 1 \\ x_{2} = 6 \\ \\ 2) \: {x}^{2} - 5x = - 6 \\ {x}^{2} - 5x + 6 = 0 \\ po \: \: teoreme \: \: vieta \\ x_{3} + x_{4} = 5\\ x_{3} x_{4} = 6\\ x_{3} =2 \\ x_{4} = 3[/tex]