Реши показательные уравнения.

Решаю показательные уравнения. Вот ответы: 1) $49^{x+1} = (\frac{1}{7})^x$ $7^{2(x+1)} = 7^{-x}$ $2x+2 = -x$ $3x = -2$ $x = -\frac{2}{3}$ 2) $4^{5x-1} = (\frac{1}{2})^{6-4x}$ $2^{2(5x-1)} = 2^{-(6-4x)}$ $10x - 2 = -6 + 4x$ $6x = -4$ $x = -\frac{2}{3}$ 3) $4^{4x-17} = 64$ $4^{4x-17} = 4^3$ $4x - 17 = 3$ $4x = 20$ $x = 5$ 4) $5^{2x-8} = 25$ $5^{2x-8} = 5^2$ $2x - 8 = 2$ $2x = 10$ $x = 5$ 5) $3^{5x+2} = 81^{x-1}$ $3^{5x+2} = 3^{4(x-1)}$ $5x + 2 = 4x - 4$ $x = -6$ 6) $4^{1-x} = (\frac{1}{2})^{3x+2}$ $2^{2(1-x)} = 2^{-(3x+2)}$ $2 - 2x = -3x - 2$ $x = -4$ 7) $27^{5-x^2} = 3^{x^2-1}$ $3^{3(5-x^2)} = 3^{x^2-1}$ $15 - 3x^2 = x^2 - 1$ $4x^2 = 16$ $x^2 = 4$ $x = \pm 2$ 8) $(\frac{1}{3})^{x-3} = 9^{2x-1}$ $3^{-(x-3)} = 3^{2(2x-1)}$ $-x + 3 = 4x - 2$ $5x = 5$ $x = 1$ **Ответы:** 1) $x = -\frac{2}{3}$ 2) $x = -\frac{2}{3}$ 3) $x = 5$ 4) $x = 5$ 5) $x = -6$ 6) $x = -4$ 7) $x = \pm 2$ 8) $x = 1