Question

ПОМОГИТЕ пожалуйста ПОДРОБНО решить

Answer 1

$2) \: \: 3x - 1 < x \\ 3x - x < 1 \\ 2x < 1 \\ x < \frac{1}{2} \\ ( - \infty . \: \frac{1}{2} )$
$4) = \frac{ {10}^{3} }{ {10}^{ log_{10}(4) } } - {( {7}^{2} )}^{ log_{7}(15) } = \frac{1000}{4} - { {7}^{ log_{7}(15) } }^{2} = 250 - {15}^{2} = 250 - 225 = 25$
$5) \: \: y = 8 - 3x \\ log_{3}(x) + log_{3}(8 - 3x) = 1 \\ log_{3}(x (8 - 3x)) = 1 \\ x(8 - 3x) = {3}^{1} \\ - 3 {x}^{2} + 8x - 3 = 0 \\ 3 {x}^{2} - 8x + 3 = 0 \\ d = {( - 8)}^{2} - 4 \times 3 \times 3 = 64 - 48 = 16 \\ \sqrt{d} = + - 4 \\ x1 = \frac{ - ( - 8) - 4}{2 \times 3} = \frac{4}{6} = \frac{2}{3} \\ x2 = \frac{ - ( - 8) + 4}{2 \times 3} = \frac{12}{6} = 2 \\ y1 = 8 - 3 \times \frac{2}{3} = 8 - 2 = 6 \\ y2 = 8 - 3 \times 6 = 8 - 18 = - 10$