327. Решить уравнение: 1) log₃ (5x - 1) = 2; 2) log₅ (3x + 1) = 2; 3) log₄ (2x - 3) = 1; 4) log₇ (x + 3) = 2; 5) lg (3x - 1) = 0; 6) lg (2 - 5x) = 1.

Решение:

Решим каждое уравнение по очереди:

1. \( \log_3 (5x - 1) = 2 \)
   \( 5x - 1 = 3^2 \)
   \( 5x - 1 = 9 \)
   \( 5x = 10 \)
   \( x = 2 \)
2. \( \log_5 (3x + 1) = 2 \)
   \( 3x + 1 = 5^2 \)
   \( 3x + 1 = 25 \)
   \( 3x = 24 \)
   \( x = 8 \)
3. \( \log_4 (2x - 3) = 1 \)
   \( 2x - 3 = 4^1 \)
   \( 2x - 3 = 4 \)
   \( 2x = 7 \)
   \( x = 3.5 \)
4. \( \log_7 (x + 3) = 2 \)
   \( x + 3 = 7^2 \)
   \( x + 3 = 49 \)
   \( x = 46 \)
5. \( \lg (3x - 1) = 0 \)
   \( 3x - 1 = 10^0 \)
   \( 3x - 1 = 1 \)
   \( 3x = 2 \)
   \( x = \frac{2}{3} \)
6. \( \lg (2 - 5x) = 1 \)
   \( 2 - 5x = 10^1 \)
   \( 2 - 5x = 10 \)
   \( -5x = 8 \)
   \( x = -1.6 \)

Ответ: 1) 2; 2) 8; 3) 3.5; 4) 46; 5) 2/3; 6) -1.6.