1)3^(х+2) + 3^х = 30
3^х ·3^2 + 3^х = 30
3^х ·9 + 3^х = 30
3^х ·(9 + 1) = 30
10·3^х = 30
3^х = 3
x = 1
2) 2/(lgx-3) + 4/(lgx+1) = 1
ОДЗ: lgx ≠ 3, lgx ≠ 1, х > 0
2·(lgx+1)/((lgx-3)·(lgx+1)) + 4·(lgx-3)/((lgx+1)(lgx-3)) = ((lgx+1)(lgx-3))/((lgx+1)(lgx-3))
2·(lgx+1) + 4·(lgx-3) = (lgx+1)(lgx-3)
2lgx + 2 + 4lgx -12 = lg²x + lgx - 3lgx - 3
6lgx -10 = lg²x - 2lgx - 3
lg²x - 8lgx + 7 = 0
Замена: у = lgx
у² - 8у + 7 = 0
D = 64 - 28 = 36
√D = 6
y₁ = (8 - 6):2 = 1
y₂ = (8 + 6):2 = 7
Возвращаемся к замене
1) 1 = lgx
х₁ = 10
2) 7 = lgx
х₂ = 10⁷ = 10 000 000