Verified answer

Ответ: x₁  = 2  ,  x₂  = -2

Объяснение:

[tex]\displaystyle \left(5^{x+4}\right) ^{x-3} = 0,2 ^x \cdot 25^{x-4} \\\\ 5^{(x+4)(x-3)} = 5^{-x} \cdot 5^{2(x-4)} \\\\ 5^{x^2 + x - 12} = 5^{x-8} \\\\ x^2 + x - 12 = x- 8 \\\\ x^2 + x - x = -8 + 12\\\\ x^2 = 4 \\\\ x_{1,2} = \pm 2[/tex]