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

- 1 + log
_{3}5/3 - log
_{5}8 - 1 + log
_{5}3/5 - log
_{5}9

### Answer

2^{x} = 3^{log5 2}

⇒ 2^{x} = 2^{log5 3}

⇒ x = log_{5} 3

⇒ x = log_{5} (3×5)/5

⇒ x = log_{5} 5 + log_{5} 3/5

⇒ x = 1 + log_{5} 3/5

**The correct option is C.**