Решение
(3^x) * (7^y) = 63
3^x + 7^y = 16
7^y = 16 - 3^x
(3^x) * (16 - 3^x) = 63
16*(3^x) - (3^2x) = 63
(3^2x) - 16*(3^x) + 63 = 0
3^x = t
t² - 16t + 63 = 0
t₁ = 7
t₂ = 9
1) 3^x = 7
log₃ (3^x) = log₃ 7
x * log₃ 3 = log₃ 7
x₁ = log₃ 7
2) 3^x = 9
3^x = 3²
x₂ = 2
Ответ: x₁ = log₃ 7 ; x₂ = 2