63^x = 7*3^(2x)
49*9^x = (7^2)*(3^(2x))
147 = 3*(7^2)
7*3^(2x) - (7^2)*(3^(2x)) - 3*(7^x) + 3*(7^2) = 0 - разделим обе части на (3*(7^2))
(3^(2x - 1))*(7^(x - 2)) - 3^(2x - 1) - 7^(x - 1) + 1 = 0
(7^(x - 2))*(3^(2x - 1) - 1) - (3^(2x - 1) - 1) = 0
(3^(2x 1) - 1)*(7^(x - 2) - 1) = 0
3^(2x - 1) = 1 = 3^0, 2x - 1 = 0, x = 1/2 = 0.5
7^(x - 2) = 1 = 7^0, x - 2 = 0, x = 2
Проверка:
x = 0.5, 63^(0.5) - 49*9^(0.5) = 3*7^(0.5) - 147; 3*√7 - 147 = 3√7 - 147 - верно
x = 2, 63^2 - 49*9^2 = 3*7^2 - 147; 3969 - 3969 = 147 - 147 - верно
Ответ: x = 0.5; x = 2