Question

помогите, пожалуйста. Логарифмы

Answer 1

$log_{2}(x - 5) times (x + 2) = 3 \ log_{2}(x {}^{2} + 2x - 5x - 10) = 3 \ x {}^{2} + 2x - 5x - 10 = 2 {}^{3} \ x {}^{2} - 3x - 10 = 8 \ x {}^{2} - 3x - 18 = 0 \ d = b {}^{2} - 4ac = 9 + 72 = sqrt{81} = 9 \ x1 = 6 \ x2 = - 3$

1) Ответ x= 6, т.к. -3 не подходит

$log_{ frac{1}{3} }(2 - x) > 1 \ 2 - x < frac{1}{3} \ - x < frac{1}{3} - 2 \ - x < - frac{5}{3} \ 2 > x > frac{5}{3}$

3) {5/3 ; 2}

$log_{2}(x - 4) < 1 \ x - 4 < 2 \ x < 2 + 4 \ 6 > x > 4$

2) {4 ; 6}