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.

1) log3 (5x - 1) = 2

5x - 1 = 3²

5x - 1 = 9

5x = 10

x = 2

Ответ: x = 2

2) log5 (3x + 1) = 2

3x + 1 = 5²

3x + 1 = 25

3x = 24

x = 8

Ответ: x = 8

3) log4 (2x - 3) = 1

2x - 3 = 4¹

2x - 3 = 4

2x = 7

x = 3.5

Ответ: x = 3.5

4) log7 (x + 3) = 2

x + 3 = 7²

x + 3 = 49

x = 46

Ответ: x = 46

5) lg (3x - 1) = 0

3x - 1 = 10⁰

3x - 1 = 1

3x = 2

x = 2/3

Ответ: x = 2/3

6) lg (2 - 5x) = 1

2 - 5x = 10¹

2 - 5x = 10

-5x = 8

x = -8/5 = -1.6

Ответ: x = -1.6