3^2x - 5*3^x+3 /3x-4 + 3^x+log₃ 5 - 27 / 3^x - 6 ≤3^x+4
3^x=t ; t>0
t²-5t+3 / t-4 + 5t-27 / t-6 - t ≤4
t²-5t+3 / t-4 - t(t-4) / t-4 + 5t-27 / t-6 ≤4
t²-5t+3-t²+4t / t-4 + 5t-27 / t-6 ≤4
3-t/t-4 + 5t-27 / t-6 ≤4
(3-t)(t-6)+(5t-27)(t-4) / (t-4)(t-6)
3t-18-t²+6t+5t²-20t-27t+108 / (t-4)(t-6) ≤ 4
4t²-38t+90 / (t-4)(t-6) ≤ 4
4t²-38t+90 - 4(t²-10t+24) / (t-4)(t-6) ≤0
-38t+40t+90-96 / (t-4)(t-6) ≤0
2(t-3) / (t-4)(t-6) ≤ 0
t=3 ; t≠4 ,t≠6 (-∞;3]∪(4;6)
3^x=3 x=1
3^x≠4 3^x≠3^log₃ 4 ;x≠log₃ 4
3^x≠6 3^x≠3^log₃ 6 ;x≠log₃ 6
Общее решение: (-∞;1]∪(log₃ 4; log₃ 6)