3x(x-1)-(x-1)=0
(x-1)(3x-1)=0
x-1=0 3x-1=0
x=1 3x=1
x=1/3
Ответ: 1/3; 1.
6x+2=5
6X=3
x=1/2
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1)у=-3/4 х+1,25;
2)у=1/3 х+2;
3)у=1,4х+2,4;
4)у=-0,5х-2
1. logx(2)−log4(x)+7/6=0, ОДЗ: x > 0
(log₂ 2 / log₂ x) - (1/2)*log₂ x + 7/6 = 0
1/(log₂ x) - (1/2)*log₂ x + 7/6 = 0
3log²₂ x - 7log₂ x - 6 = 0
Пусть log₂ x = z
3z² - 7z - 6 = 0
D = 49 + 4*3*6 = 121
z₁ = (7 - 11)/6 = - 1/3
z₂ = (7 + 11)/6 = 3
1) log₂ x = - 1/3
x = 2^(-1/3)
x₁ = 1/∛2
2) log₂ x = 3
x₂ = 2³
x₂ = 8
2. log₃ <span>(3^x−8 )= 2 - x, </span>ОДЗ: 3^x - 8 > 0, 3^x > 8, x > log₃ 8<span>
3^x - 8 = 3^(2 - x)
3^x - 8 = 9*(1/3^x)
3^(2x) - 8*(3^x) - 9 = 0
Пусть 3^x = z
z</span>² - 8z - 9 = 0
z₁ = -1
z₂ = 9
<span>1) 3^x = - 1, не имеет смысла
2) 3^x = 9
3^x = 3</span>²
<span>x = 2
</span>