Решение
3*4^×+2*9^×=5*6^×
3*(2^2x) +2*(3^2x) - 5*(2^x)*(3^x) = 0 делим на (2^x)*(3^x)
3*(2/3)^x + 2*(1/(2/3)^x) - 5 = 0
(2/3)^x = t
3t + 2/t - 5 = 0
3t² - 5t + 2 = 0
D = 25 - 4*3*2 = 1
t₁ = (5 - 1)/6
t₁ = 2/3
t₂ = (5 + 1)/6
t₂ = 1
1) (2/3)^x = 2/3
x₁ = 1
2) (2/3)^x = 1
(2/3)^x = (2/3)⁰
x₂ = 0