24) 4 * 2^{2x} - 6^x = 18 * 3^{2x}

4 * 2^{2x} - 6^x = 18 * 3^{2x} 4 * 2^{2x} - (2*3)^x = 18 * 3^{2x} 4 * (2^x)^2 - 2^x * 3^x = 18 * (3^x)^2 Разделим обе части на (3^x)^2 4 * (2^x / 3^x)^2 - (2^x / 3^x) = 18 Пусть y = (2/3)^x. 4y^2 - y = 18 4y^2 - y - 18 = 0 D = (-1)^2 - 4 * 4 * (-18) = 1 + 288 = 289 y_1 = (1 + √289) / (2 * 4) = (1 + 17) / 8 = 18 / 8 = 9/4 y_2 = (1 - √289) / (2 * 4) = (1 - 17) / 8 = -16 / 8 = -2 Вернёмся к замене: (2/3)^x = 9/4 (2/3)^x = (3/2)^2 = (2/3)^{-2} x = -2 (2/3)^x = -2 Нет решений Ответ: x = -2