If x is a real number such that log_{3} 5 = log_{5} (2 + x), then which of the following is true?

- 0 < x < 3
- 23 < x < 30
- x > 30
- 3 < x < 23

### Answer

log_{3} 5 = log_{5} (x + 2)

log_{3} 3 < log_{3} 5 < log_{3} 9

1 < log_{3} 5 < 2

So, 1 < log_{5} (x + 2) < 2

5^{1} < x + 2 < 5^{2}

3 < x < 23

**The correct option is D.**