10-11 класс логарифмические уравнения,задание во вложениях

$1) \ log_x2 + log_{4x}4 = 1\\\\ 1/log_2x + 2/log_24x = 1\\\\ log_24x + 2log_2x = log_24xlog_2x\\\\ log_24x + 2log_2x - log_24xlog_2x = 0\\\\ log_24x(1 - log_2x)+2log_2x = 0\\\\ (log_24+log_2x)(1 - log_2x) + 2log_2x = 0\\\\ (2+log_2x)(1 - log_2x) + 2log_2x = 0\\\\ 2 - log^2_2x - log_2x + 2log_2x = 0\\\\ -log^2_2x + log_2x + 2 = 0 log_2x = t\\\\ -t^2+t+2 = 0\\\\ t = -1, t = 2\\\\ log_2x = -1, x = 1/2\\\\ log_2x = 2, x = 4\\\\ x_1*x_2 = 2\\\\$

$2) \ lg(x+11)-1/2lg(2x+7) = 2-lg25\\\\ lg(25(x+11)/\sqrt{2x+7}) = lg100\\\\ 25(x+11)/\sqrt{2x+7} = 100\\\\ (x+11) = 4\sqrt{2x+7}\\\\ x^2 + 22x + 121 = 16(2x + 7)\\\\ x^2 - 10x + 121 - 16*7 = 0\\\\ x_1 + x_2 = 10\\\\$

$3) \ log_2(54-x^3) = 3log_2x\\\\ 54 - x^3 = x^3\\\\ x^3 = 27\\\\ x = 3\\\\$