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

Logarithms
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.**