Вариант № 9 1. Решить уравнения: (1/7)^(5+x) = 49 4^(1+x) = 64 8^(11-5x) = 64^x 3^(1-3x) = 1,5*2^(1-3x) 2^(4x-14) = 1/64 (1/2)^(18-3x) = 64 (1/25)^(1+x) = 125^(-1)

1. Решить уравнения:

1. $$\left(\frac{1}{7}\right)^{5+x} = 49$$ $$\left(7^{-1}\right)^{5+x} = 7^2$$ $$7^{-5-x} = 7^2$$ $$-5-x = 2$$ $$-x = 7$$ $$x = -7$$

   Ответ: -7

2. $$4^{1+x} = 64$$ $$4^{1+x} = 4^3$$ $$1+x = 3$$ $$x = 2$$

   Ответ: 2

3. $$8^{11-5x} = 64^x$$ $$(2^3)^{11-5x} = (2^6)^x$$ $$2^{33-15x} = 2^{6x}$$ $$33-15x = 6x$$ $$21x = 33$$ $$x = \frac{33}{21}$$ $$x = \frac{11}{7}$$

   Ответ: 11/7

4. $$3^{1-3x} = 1.5 \cdot 2^{1-3x}$$ $$\frac{3^{1-3x}}{2^{1-3x}} = 1.5$$ $$\left(\frac{3}{2}\right)^{1-3x} = \frac{3}{2}$$ $$1-3x = 1$$ $$-3x = 0$$ $$x = 0$$

   Ответ: 0

5. $$2^{4x-14} = \frac{1}{64}$$ $$2^{4x-14} = 2^{-6}$$ $$4x-14 = -6$$ $$4x = 8$$ $$x = 2$$

   Ответ: 2

6. $$\left(\frac{1}{2}\right)^{18-3x} = 64$$ $$\left(2^{-1}\right)^{18-3x} = 2^6$$ $$2^{-18+3x} = 2^6$$ $$-18+3x = 6$$ $$3x = 24$$ $$x = 8$$

   Ответ: 8

7. $$\left(\frac{1}{25}\right)^{1+x} = 125^{-1}$$ $$\left(5^{-2}\right)^{1+x} = (5^3)^{-1}$$ $$5^{-2-2x} = 5^{-3}$$ $$-2-2x = -3$$ $$-2x = -1$$ $$x = \frac{1}{2}$$

   Ответ: 1/2