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

Answer

2^x = 3^{log₅ 2}

⇒ 2^x = 2^{log₅ 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.