If x is a real number such that log3 5 = log5 (2 + x)

• Logarithms

If x is a real number such that log₃ 5 = log₅ (2 + x), then which of the following is true?

1. 0 < x < 3
2. 23 < x < 30
3. x > 30
4. 3 < x < 23

Answer

log₃ 5 = log₅ (x + 2)

log₃ 3 < log₃ 5 < log₃ 9

1 < log₃ 5 < 2

So, 1 < log₅ (x + 2) < 2

5¹ < x + 2 < 5²

3 < x < 23

The correct option is D.