a)
[tex](4^{5}\cdot x-32^{2})\cdot2^{5}=2^{16}\cdot x \ \ /:2^{5}\\\\4^{5}\cdot x-32^{2} =2^{11}\cdot x\\\\(2^{2})^{5}x - (2^{5})^{2} = 2^{11}x\\\\2^{10}x - 2^{10} = 2^{11}x\\\\2^{10}(x-1) = 2^{11}x \ \ /:2^{10}\\\\x-1 = 2x\\\\x-2x = 1\\\\-x = 1 \ \ /:(-1)\\\\\boxed{x = -1 }[/tex]
d)
[tex]1 - \frac{x-36}{3} \geq (3x-2)^{2}-9(x+1)(x-1) \ \ /\cdot3\\\\3-(x-36) \geq 3(3x-2)^{2}-27(x+1)(x-1)\\\\3-x+36 \geq 3(9x^{2}-12x+4)-27(x^{2}-1)\\\\-x+39\geq 27x^{2}-36x+12 - 27x^{2}+27\\\\-x+39 \geq -36x+39\\\\-x+36x \geq 39-39\\\\35x \geq 0 \ \ /:35\\\\\boxed{x \geq 0}\\\\\underline{x \in \langle0;+\infty)}[/tex]
e)
[tex]log_{3}3^{2-3x} < (2x+1)[log_{5}2 - log_{5}10]\\\\2-3x < (2x+1)\cdot log_{5}\frac{2}{10}\\\\2-3x< (2x+1)\cdot log_{5}\frac{1}{5}\\\\2-3x< (2x+1)\cdot log_{5}5^{-1}\\\\2-3x < (2x+1)\cdot(-1)\\\\2-3x < -2x-1\\\\-3x +2x < -1-2\\\\-x < -3 \ \ /:(-1)\\\\\boxed{x > 3}\\\\\underline{x \in (3;+\infty)}[/tex]
