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.