277 Решить уравнение: 1) log6 x = 3; 2) log5 x = 4; 3) log2 (5 - x) = 3; 4) log3 (x + 2) = 3; 1 5) log₁ (0,5 + x) = -1. 6

1. $$log_6 x = 3$$ $$x = 6^3$$ $$x = 216$$
2. $$log_5 x = 4$$ $$x = 5^4$$ $$x = 625$$
3. $$log_2 (5 - x) = 3$$ $$5 - x = 2^3$$ $$5 - x = 8$$ $$x = 5 - 8$$ $$x = -3$$
4. $$log_3 (x + 2) = 3$$ $$x + 2 = 3^3$$ $$x + 2 = 27$$ $$x = 27 - 2$$ $$x = 25$$
5. $$log_{\frac{1}{6}} (0,5 + x) = -1$$ $$0,5 + x = (\frac{1}{6})^{-1}$$ $$0,5 + x = 6$$ $$x = 6 - 0,5$$ $$x = 5,5$$

Ответ: 1) $$x = 216$$ 2) $$x = 625$$ 3) $$x = -3$$ 4) $$x = 25$$ 5) $$x = 5,5$$