Question

помогите решить уравнения:

$1.log_ frac{1}{2} (3x-4)= log_ frac{1}{2} (5x-1) 2.log _{2} ( x^{2} +4x+4)=4 3.lg_ frac{1}{2} x+ lg x-2=0$

Answer 1

1) 
3x - 4 = 5x-1
-2x = 3
x = $frac{-3}{2}$

2)
$log_{2}(x^2+4x + 4) = log_{2}16 \ x^2+4x + 4 = 16 \ x^2+4x -12 = 0 \ D = 16 + 48 = 64\ x_1 = frac{-4+8}{2} = 2\ x_2 = frac{-4-8}{2} = -6$

3)
$lg^2x + lgx - 2 = 0\ lgx = t\ t^2 + t - 2 = 0\D = 1 + 8 = 9\x_1 = frac{-1+3}{2} = 1\ x_2 = frac{-1-3}{2} = -2\ (1) lgx = 1 \ x = 10 \ (2)lgx = -2\x = 10^{-2}$

Answer 2

спасибо )

Answer 3

Не за что)