Решение
1) 2^(5x - 4) = 2^(4x + 12)
5x - 4 = 4x + 12
x = 16
2) 3^x = t, t > 0
t² - 2t - 3 = 0
t₁ = 3
t₂ = - 1 не удовлетворяет условию: t > 0
3^x = 3
x = 1
3) 3*3^2x - 3^2x - 53*3^x - 27 = 0
2*(3^2x) + 53*(3^x) - 27 = 0
3^x = z, z > 0
2z² - 53z - 27 = 0
D = 2809 + 4*2*27 = 3025
z₁ = ( 53 + 55)/4
z₁ = 108 /4
z₁ = 27
z₂ = ( 53 - 55)/4
z₂ = - 1/2 не удовлетворяет условию: z > 0
3^x = 27
3^x = 3³
x = 3