Решите уравнения1                            4_____      +   ____________       = -1lg (9x - 8)      lg (9x - 8) + lg 0,001 4                            6_________     +   ___________  = -5lg (3x - 5) + 2      lg (3x - 5) - 36 ...

1) lg (9x-8) = a [latex] \frac{1}{a} + \frac{4}{a-3} = -1[/latex] a - 3 + 4a = -a² + 3a a² + 2a - 3 = 0 a₁ = 1 a₂ = -3 lg (9x-8) = 1 9x-8 = 10 x = 2 lg (9x-8) = -3 9x - 8 = 0.001 x = 0.889 2) lg (3x-5) = a [latex] \frac{4}{a+2} + \frac{6}{a-3} = -5[/latex] 4a-12 + 6a+12 = -5(a+2)(a-3) 10a = -5 (a² - a - 6) -2a = a² - a - 6 a² + a - 6=0 D= 1+24=25 a₁ = 2 a₂ = -3 lg (3x-5) = 2 3x-5 = 100 x = 35 lg (3x-5) = -3 3x-5 = 0.001 x = 1.667 3) lg (x-7) = a [latex] \frac{6}{a+2} - \frac{6}{a-3} = 5[/latex] 6a- 18 - 6a- 12= 5(a+2)(a-3) -30 = 5(a² - a - 6) -6 = a² - a -6 a² - a = 0 a(a-1) = 0 a=0 a=1 lg(x+7) = 0 x+7=1 x= -6 lg (x+7) = 1 x+7=10 x=3