Question

решите уравнения

1                            4
_____      +   ____________       = -1
lg (9x - 8)      lg (9x - 8) + lg 0,001 


4                            6
_________     +   ___________  = -5
lg (3x - 5) + 2      lg (3x - 5) - 3


6                          6
_________      -   ____________   = 5
lg (x + 7) + 2       lg (x + 7) - 3

Answer 1

1) lg (9x-8) = a
$frac{1}{a} + frac{4}{a-3} = -1$
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
$frac{4}{a+2} + frac{6}{a-3} = -5$

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
$frac{6}{a+2} - frac{6}{a-3} = 5$
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