Найдите корень уравнения \sqrt{\frac{7}{4x - 57}} = \frac{1}{3}

5. **Ответ: 30** $$\sqrt{\frac{7}{4x - 57}} = \frac{1}{3}$$ $$\frac{7}{4x - 57} = \frac{1}{9}$$ $$4x - 57 = 63$$ $$4x = 120$$ $$x = 30$$ 6. **Ответ: 6** $$9^{6 + x} = 81^{2x}$$ $$9^{6 + x} = (9^2)^{2x}$$ $$6 + x = 4x$$ $$3x = 6$$ $$x = 2$$ 7. **Ответ: 4** $$(\frac{1}{2})^{6 - 2x} = 4$$ $$2^{-(6 - 2x)} = 2^2$$ $$-6 + 2x = 2$$ $$2x = 8$$ $$x = 4$$ 8. **Ответ: -0,5** $$4^{1 - 2x} = 64$$ $$4^{1 - 2x} = 4^3$$ $$1 - 2x = 3$$ $$-2x = 2$$ $$x = -1$$ 9. **Ответ: 4** $$2^{4x - 19} = \frac{1}{8}$$ $$2^{4x - 19} = 2^{-3}$$ $$4x - 19 = -3$$ $$4x = 16$$ $$x = 4$$ 10. **Ответ: -0,4** $$9^{3 + 5x} = 0,81 \cdot 10^{3 + 5x}$$ $$\frac{9^{3 + 5x}}{10^{3 + 5x}} = 0,81$$ $$0,9^{3 + 5x} = 0,9^2$$ $$3 + 5x = 2$$ $$5x = -1$$ $$x = -0,2$$ 11. **Ответ: 4** $$(\frac{1}{4})^{3x - 5} \cdot (\frac{1}{4})^{1 - 2x} = 1$$ $$(\frac{1}{4})^{3x - 5 + 1 - 2x} = (\frac{1}{4})^0$$ $$x - 4 = 0$$ $$x = 4$$ 12. **Ответ: 1** $$(\frac{1}{2})^{4x - 3} : (\frac{1}{2})^x = 1$$ $$(\frac{1}{2})^{4x - 3 - x} = (\frac{1}{2})^0$$ $$3x - 3 = 0$$ $$3x = 3$$ $$x = 1$$