3. Решить уравнение: 1) log₄ (2x+3) = 3 2) log₃(x-8)+ log₃ 8 = 2 3) log₃\(\u\)207A x + log₉ x = 10

Решение:

1. \( \log_4 (2x+3) = 3 \)
   \( 2x+3 = 4^3 \)
   \( 2x+3 = 64 \)
   \( 2x = 61 \)
   \( x = 30.5 \)
   Проверка: \( 2(30.5) + 3 = 61 + 3 = 64 > 0 \).
2. \( \log_3 (x-8) + \log_3 8 = 2 \)
   \( \log_3 (8(x-8)) = 2 \)
   \( 8(x-8) = 3^2 \)
   \( 8x - 64 = 9 \)
   \( 8x = 73 \)
   \( x = \frac{73}{8} = 9.125 \)
   Проверка: \( x-8 = 9.125 - 8 = 1.125 > 0 \).
3. \( \log_{\sqrt{3}} x + \log_9 x = 10 \)
   \( \log_{3^{1/2}} x + \log_{3^2} x = 10 \)
   \( 2 \log_3 x + \frac{1}{2} \log_3 x = 10 \)
   \( (2 + \frac{1}{2}) \log_3 x = 10 \)
   \( \frac{5}{2} \log_3 x = 10 \)
   \( \log_3 x = 10 \cdot \frac{2}{5} = 4 \)
   \( x = 3^4 = 81 \)
   Проверка: \( x > 0 \).

Ответ: 1) 30.5; 2) \(\frac{73}{8}\); 3) 81.