Logarithms

If x is a positive quantity such that 2x = 3log5 2, then x is equal to

  1. 1 + log3 5/3
  2. log5 8
  3. 1 + log5 3/5
  4. log5 9

Answer

2x = 3log5 2

⇒ 2x = 2log5 3

⇒ x = log5 3

⇒ x = log5 (3×5)/5

⇒ x = log5 5 + log5 3/5

⇒ x = 1 + log5 3/5

The correct option is C.