27*81^sinx-12*9^sinx +1=0 [3pi/2;3pi]

Question

27*81^sinx-12*9^sinx +1=0
[3pi/2;3pi]

Answer 1

9^sinx = t

27t² - 12t + 1 = 0
D = 144 - 108 = 36
t1 = (12 - 6)/54 = 1/9

t2 = (12 + 6)/54 = 1/3

9^sinx = 1/9
sinx = -1

x1 = 3π/2

9^sinx = 1/3
sinx = -0.5

x2 = 11π/6

Ответ: 3π/2; 11π/6