514. a) log: (2x-4)=-2; 2 B) log0,3 (5+2x)=1; 6) log (x²+2x+3)=logx 6; r) log2 (3-x)=0.

Ответ: a) x = 2.25; б) x = -1.15; в) x = -3 и x = 1; г) x = 2

Решаем каждое уравнение:

1. a) \( \log_{\frac{1}{2}} (2x - 4) = -2 \) \( \Rightarrow 2x - 4 = (\frac{1}{2})^{-2} = 4 \) \( \Rightarrow 2x = 8 \) \( \Rightarrow x = 4 \)
2. б) \( \log_{0.3} (5 + 2x) = 1 \) \( \Rightarrow 5 + 2x = 0.3 \) \( \Rightarrow 2x = -4.7 \) \( \Rightarrow x = -2.35 \)
3. в) \( \log_x (x^2 + 2x + 3) = \log_x 6 \) \( \Rightarrow x^2 + 2x + 3 = 6 \) \( \Rightarrow x^2 + 2x - 3 = 0 \) \( \Rightarrow (x + 3)(x - 1) = 0 \) \( \Rightarrow x = -3 \) и \( x = 1 \)
4. г) \( \log_2 (3 - x) = 0 \) \( \Rightarrow 3 - x = 1 \) \( \Rightarrow x = 2 \)

Ответ: a) x = 2.25; б) x = -1.15; в) x = -3 и x = 1; г) x = 2